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C₂²×#37614 #72300990

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

Aliases

Subgroups

127533 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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