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C₂×#36711 #7634140

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

Aliases

Subgroups

8950 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7541336);