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C₂²×#42420 #72291837

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

Aliases

Subgroups

120305 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 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((11,15)(14,16)(18,19)(20,24), (17,18,21,19)(20,23,24,22), (10,13)(14,16)(18,19)(22,23), (6,8)(9,10)(11,14)(12,13)(15,16)(17,19,21,18)(20,23,24,22), (5,6,7,8)(9,11,12,15)(10,14,13,16)(17,20,21,24)(18,22,19,23), (3,4), (1,2)(3,4));