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C₂×#12987 #494429

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

Aliases

Subgroups

1274 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 66 points:

(1,2);(3,4,8,15,9,16,30,45,10,13,31,32,7,14,27,42)(5,11,20,35,19,34,51,61,18,36,28,43,25,40,56,63)(6,21,24,54,23,39,55,44,22,41,29,57,26,12,37,38)(17,46,48,64,49,33,58,60,50,53,52,66,47,59,65,62);(3,5,8,28,9,19,30,56,10,18,31,20,7,25,27,51)(4,11,32,35,16,34,42,61,13,36,15,43,14,40,45,63)(6,17,29,48,23,49,37,58,22,50,24,52,26,47,55,65)(12,33,38,62,21,53,54,64,39,59,44,60,41,46,57,66);(3,6)(4,12)(5,17)(7,26)(8,29)(9,23)(10,22)(11,33)(13,39)(14,41)(15,44)(16,21)(18,50)(19,49)(20,52)(24,31)(25,47)(27,55)(28,48)(30,37)(32,38)(34,53)(35,62)(36,59)(40,46)(42,54)(43,60)(45,57)(51,65)(56,58)(61,64)(63,66)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401625);