Finite Group Databasebeta

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C₂⁴×#551 #72295505

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

Aliases

Subgroups

633253 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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