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C₂²×#10987 #72314647

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

Aliases

Subgroups

49277 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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