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C₂×#491 #3134

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

Aliases

Subgroups

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

32 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 1866);