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C₂×#93995 #72319941

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

Aliases

Subgroups

665 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 66 points:

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

Conjugacy classes & character table

184 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((4,10,11,25,13,27,30,49)(6,19,20,44)(7,22)(12,32,33,26,34,51,29,52)(14,37,31,56,36,28,54,50)(15,38,39,63)(16,41)(21,47,46,45)(23,48)(35,60,58,62,59,57,55,53)(40,65,61,64)(42,66), (1,2), (3,4,6,12,7,14,21,35,8,11,19,29,23,31,45,55,9,13,20,34,22,36,46,59,24,30,44,33,48,54,47,58)(5,10,15,26,16,28,40,53,17,25,38,32,42,50,64,57,18,27,39,52,41,37,61,62,43,49,63,51,66,56,65,60));