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C₂×#12742 #493537

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

Aliases

Subgroups

3112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400733);