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C₂×#2356 #34119

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

Aliases

Subgroups

1275 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27107);