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C₂⁴×#3543 #72295521

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

Aliases

Subgroups

10370760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 9 generators on 24 points:

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

Conjugacy classes & character table

608 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((9,10,12,13)(11,15,16,14)(17,18,23,22)(19,24,21,20), (9,10)(11,14)(12,13)(15,16)(17,19,23,21)(18,24,22,20), (10,13)(14,15)(17,20)(18,21)(19,22)(23,24), (9,11,12,16)(10,14,13,15)(17,21,23,19)(18,24,22,20), (9,10)(11,14)(12,13)(15,16)(17,22,23,18)(19,24,21,20), (3,4), (5,6), (7,8), (1,2)(3,4)(5,6)(7,8));