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C₂×#36965 #7634237

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

Aliases

Subgroups

9798 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7541433);