Finite Group Databasebeta

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C₂×#72224976 #72320977

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

Aliases

Subgroups

2064 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

164 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((4,11,14,41,16,43,38,44)(5,18,21,56,24,57,26,63)(6,27,30,20)(7,12)(8,36)(9,35)(13,46)(15,48,17,55,37,28,33,42)(19,59,60,66)(22,34,47,45,29,23,58,25)(31,39,62,32)(40,64,49,61)(50,54)(52,53), (1,2), (3,4,12,15,9,38,7,33,10,16,8,37,35,14,36,17)(5,19,23,59,21,61,25,49,24,60,34,66,26,64,45,40)(6,28,27,43,32,42,62,44,30,48,20,11,39,55,31,41)(13,47,65,57,52,22,54,56,53,58,51,18,46,29,50,63), (3,5,20,57,36,23,6,29,35,21,62,56,8,25,39,47,10,24,27,18,7,34,30,22,9,26,31,63,12,45,32,58)(4,13,48,60,37,50,11,40,38,46,55,61,17,51,41,66,16,53,28,19,15,54,43,49,14,52,42,64,33,65,44,59));