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C₂×#12615 #492972

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

Aliases

Subgroups

1102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

(1,2);(3,4)(5,6)(7,8,11,17,12,16,24,31,13,18,25,32,10,14,23,27)(9,15,21,29,22,28,35,37,19,30,33,38,20,26,34,36);(4,6)(8,14,18,16)(9,19)(15,28,30,26)(17,27,32,31)(20,22)(21,33)(29,37,38,36)(34,35);(7,9,11,21,12,22,24,35,13,19,25,33,10,20,23,34)(8,15,17,29,16,28,31,37,18,30,32,38,14,26,27,36)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400168);