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C₂²×#13937 #72340081

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

Aliases

Subgroups

259557 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

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

Conjugacy classes & character table

304 conjugacy classes. The character table is too large to display.

Relationships

GAP

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

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