Finite Group Databasebeta

?

← Prev (#7622847) Next (#7622849) →

C₂×#33542 #7622848

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

Aliases

Subgroups

3822 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530044);