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C₂×#3126 #60555

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

Aliases

Subgroups

1061 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 53543);