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C₂×#10672 #243936

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

Aliases

Subgroups

1320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 151132);