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C₂×#34391 #7625947

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

Aliases

Subgroups

9006 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)(16,20)(17,23)(22,27)(24,29);(8,11)(12,13)(16,20)(21,26)(22,27)(28,30);(15,16,19,20)(17,21,23,26)(18,22,25,27)(24,28,29,30);(7,8)(9,12)(10,11)(13,14)(15,17)(16,21)(18,24)(19,23)(20,26)(22,28)(25,29)(27,30);(7,9)(8,12)(10,14)(11,13)(15,18,19,25)(16,22,20,27)(17,24,23,29)(21,28,26,30)

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7533143);