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C₂×#2651 #34580

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

Aliases

Subgroups

1111 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27568);