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C₂²×#36317 #72300959

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

Aliases

Subgroups

113665 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

280 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)(9,10,14,12)(11,13,15,16), (5,6)(7,8)(9,11,14,15)(10,13,12,16)(17,18)(19,22)(20,23)(21,24), (17,19)(18,21)(20,24)(22,23), (9,12,14,10)(11,13,15,16)(17,19)(18,22)(20,24)(21,23), (9,13)(10,15)(11,12)(14,16)(17,18)(19,21)(20,23)(22,24), (3,4), (1,2)(3,4));