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C₂²×#11004 #72314712

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

Aliases

Subgroups

49237 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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