Finite Group Databasebeta

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C₂×#152284 #72320002

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

Aliases

Subgroups

1519 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

124 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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