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C₂×#33465 #7622625

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

Aliases

Subgroups

1904 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 66 points:

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

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, 7529821);