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C₂×#13192 #495089

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

Aliases

Subgroups

1190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402285);