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C₂²×#8062966 #72301202

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

Aliases

Subgroups

1239812 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 24 points:

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

Conjugacy classes & character table

380 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)(9,10)(11,15)(12,13)(14,16)(19,23)(20,24), (5,6)(7,8)(9,10)(11,14)(12,13)(15,16)(17,18)(19,20)(21,22)(23,24), (9,10)(11,15)(12,13)(14,16)(17,19,21,23)(18,20,22,24), (10,13)(14,15)(18,22)(19,23), (9,10)(11,14)(12,13)(15,16)(17,20)(18,19)(21,24)(22,23), (9,11)(10,14)(12,16)(13,15)(17,19)(18,20)(21,23)(22,24), (3,4), (1,2)(3,4));