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C₂×#2612 #34870

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

Aliases

Subgroups

1015 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27858);