Super Galaxy Dai-Gurren is a titanic Gunmen warship that once served Lordgenome as the flagship Cathedral Terra before disguising itself as the moon. Reclaimed by Simon, it becomes Team Dai-Gurren's flagship for the war against the Anti-Spiral.
Super Galaxy Dai-Gurren is an immense Gunmen warship on the scale of the Arc-Gurren. It flickers into view during the prologue of the very first episode, long before it is properly introduced near the close of the story's third act. In an earlier age the vessel went by the name Cathedral Terra and served as the flagship Lordgenome commanded against the Anti-Spirals. After Lordgenome was bent to the enemy's will and installed as king of Earth, the ship took on the shape of the moon and kept watch, ready to report any sign of Spiral activity on the planet below.
The warship's fighting strength has no equal among the other vessel-type mecha of the series, packing a staggering spread of missiles, beam weapons, and defensive shielding. It can cross between separate worlds and universes, and it holds the industrial capacity to churn out hundreds of Arc-Gurren Lagann-sized machines in short order. Its sheer bulk forces the crew to rely on internal transport systems just to move around inside. Among its tools are the Dimensional Anchors, which drive into imaginary space. In the climactic fight, Simon gathered enough Spiral Power, drawing on the strength of those who came before him, to reshape the ship into a towering humanoid he named the Transcendent Super Spiral Dreadnought Gunmen: Super Galaxy Gurren Lagann, sweeping the enemy away.
Lordgenome held the ship first, wielding it as Cathedral Terra in his war on the Anti-Spirals before his defection. Its true nature stayed hidden until the decisive clash during the Anti-Spiral assault on the Arc-Gurren, when Cathedral Terra shed its lunar disguise and turned on the Spirals. Simon beat it and won it back for Team Dai-Gurren, and from then on it carried them as their flagship on the campaign to bring down the Anti-Spiral and rescue Nia. In Parallel Works part 8, which looks at Lordgenome's days as a Spiral Warrior, the same vessel appears in Gunmen mode as Cathedral Lazengann, resembling Lazengann and lacking the star sunglasses, used to annihilate the human race and even shown performing a Giga Drill Break.

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Super Galaxy Dai-Gurren was once Cathedral Terra, the flagship Lordgenome commanded against the Anti-Spirals. After his defection it disguised itself as the moon and watched Earth for signs of Spiral activity.
Simon reshapes Super Galaxy Dai-Gurren into a towering humanoid he names Super Galaxy Gurren Lagann, using Spiral Power drawn from the strength of those who came before him.
The Dimensional Anchors are among Super Galaxy Dai-Gurren's tools, weapons that drive into imaginary space.
Simon serves as captain of Super Galaxy Dai-Gurren, leading Team Dai-Gurren aboard it as their flagship in the war against the Anti-Spiral.
Cathedral Lazengann is the same vessel's Gunmen form as seen in Parallel Works part 8, set during Lordgenome's era as a Spiral Warrior, resembling Lazengann without the star sunglasses and used to annihilate the human race.
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