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C₂²×#35227 #72337192

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

Aliases

Subgroups

113181 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 24 points:

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

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((17,18,21,19)(20,22,24,23), (5,6,7,8)(11,15)(13,16)(18,19)(20,24), (5,6)(7,8)(9,10,12,14)(11,16,15,13)(17,19,21,18)(20,22,24,23), (3,4), (17,20)(18,22)(19,23)(21,24), (1,2)(3,4), (9,11)(10,13)(12,15)(14,16));