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C₂⁴×#560 #72295508

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

Aliases

Subgroups

635397 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 24 points:

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

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