Finite Group Databasebeta

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C₂⁴×#559 #72295510

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

Aliases

Subgroups

554821 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

400 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)(11,14)(12,13)(15,16)(18,21)(19,23), (9,11,13,16)(10,14,12,15)(17,18)(19,24)(20,21)(22,23), (9,11)(10,15)(12,14)(13,16)(17,19)(18,22)(20,23)(21,24), (9,12,13,10)(11,14,16,15)(17,18)(19,24)(20,21)(22,23), (3,4), (5,6), (7,8), (1,2)(3,4)(5,6)(7,8));