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C₂²×#10984 #72314579

• 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:

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

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