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C₂×#12871 #493910

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

Aliases

Subgroups

1234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401106);