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C₂×#2496 #34760

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

Aliases

Subgroups

1287 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27748);