Finite Group Databasebeta

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C₂⁴×#553 #72295501

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

Aliases

Subgroups

559733 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)(17,18,20,22)(19,21,24,23);(10,13)(11,15)(17,18,20,22)(19,23,24,21);(9,10)(11,14)(12,13)(15,16)(17,18)(19,21)(20,22)(23,24);(9,11,12,15)(10,14,13,16)(17,19,20,24)(18,21,22,23);(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)(17,18,20,22)(19,21,24,23), (10,13)(11,15)(17,18,20,22)(19,23,24,21), (9,10)(11,14)(12,13)(15,16)(17,18)(19,21)(20,22)(23,24), (9,11,12,15)(10,14,13,16)(17,19,20,24)(18,21,22,23), (3,4), (5,6), (7,8), (1,2)(3,4)(5,6)(7,8));