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C₂²×#11012 #72314602

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

Aliases

Subgroups

47781 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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