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C₂×#2828 #36666

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

Aliases

Subgroups

1411 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 29654);