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C₂×#3333 #61153

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

Aliases

Subgroups

1105 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54141);