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C₂×#3136 #60610

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

Aliases

Subgroups

1131 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)(14,21)(17,24)(18,23)(20,25);(4,7)(8,10)(11,12,14,16,15,18,21,23)(13,17,19,22,20,24,25,26);(3,5,6,9)(4,8,7,10)(11,13,14,19,15,20,21,25)(12,17,16,22,18,24,23,26);(12,18)(16,23)(17,24)(22,26)

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, 53598);