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C₂×#13198 #495105

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

Aliases

Subgroups

1104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402301);