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C₂²×#11030 #72314657

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

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