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C₂²×#59142 #72300964

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

Aliases

Subgroups

116141 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 24 points:

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

Conjugacy classes & character table

256 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), (5,6)(7,8)(9,10)(11,14)(12,15)(13,16)(17,18,21,23)(19,20,22,24), (9,11)(10,13)(12,16)(14,15)(17,19,21,22)(18,20,23,24), (9,11)(10,14)(12,16)(13,15)(17,19)(18,20)(21,22)(23,24), (9,10)(11,13)(12,15)(14,16)(17,20)(18,22)(19,23)(21,24), (3,4), (1,2)(3,4));