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C₂×#47953 #7704004

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

8248 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 30 points:

(1,2);(4,6)(15,16,20,18)(17,22,25,21)(19,26,28,23)(24,29,27,30);(7,8)(9,13)(10,14)(11,12)(15,17,20,25)(16,21,18,22)(19,27,28,24)(23,30,26,29);(3,4,5,6)(8,12)(9,14)(15,17)(16,22)(18,21)(19,24)(20,25)(23,30)(26,29)(27,28);(7,9)(8,10)(11,14)(12,13)(15,18,20,16)(17,22,25,21)(19,26,28,23)(24,30,27,29);(7,10)(8,9)(11,13)(12,14)(15,19,20,28)(16,23,18,26)(17,24,25,27)(21,29,22,30)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7611200);