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C₂×#2627 #34558

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

Aliases

Subgroups

1447 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 27546);