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C₂×#9668 #204427

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

Aliases

Subgroups

1408 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

(1,2);(3,4,6,9,7,5,8,10)(11,12,16,20,17,19,15,13)(14,22,24,26,25,21,23,18);(3,5,6,10,7,4,8,9)(11,13,16,19,17,20,15,12)(14,21,24,26,25,22,23,18);(11,14,16,24,17,25,15,23)(12,18,13,21,19,26,20,22)

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, 111623);