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C₂²×#612802 #72296108

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

Aliases

Subgroups

2957152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

464 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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