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C₂×#3137 #60611

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

Aliases

Subgroups

1035 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)(11,12,16,18)(13,19,20,26)(14,15,22,23)(17,24,25,21);(4,7)(8,10)(11,13,15,21,16,20,23,24)(12,17,14,19,18,25,22,26);(3,5,6,9)(4,8,7,10)(11,14,15,18,16,22,23,12)(13,19,21,25,20,26,24,17);(13,20)(17,25)(19,26)(21,24)

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, 53599);