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C₂²×#34379 #72300996

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

Aliases

Subgroups

116845 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

304 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((5,6,7,8)(9,10)(11,14)(12,15)(13,16)(17,18)(19,22)(20,23)(21,24), (9,11)(10,13)(12,16)(14,15), (9,10,12,15)(11,13,16,14)(17,19,20,24)(18,21,23,22), (9,10)(11,13)(12,15)(14,16)(17,18)(19,21)(20,23)(22,24), (9,11)(10,14)(12,16)(13,15)(17,19)(18,22)(20,24)(21,23), (3,4), (1,2)(3,4));