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C₂²×#7664581 #72325850

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

Aliases

Subgroups

1641672 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

440 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((11,15)(14,16)(17,18)(19,22)(20,23)(21,24), (11,15)(14,16)(17,19)(18,21)(20,24)(22,23), (9,10)(11,14)(12,13)(15,16), (3,4), (5,6,7,8)(10,13)(14,16)(17,19)(18,22)(20,24)(21,23), (1,2)(3,4), (9,10)(11,16)(12,13)(14,15), (5,6)(7,8)(9,11)(10,14)(12,15)(13,16)(17,18)(19,21)(20,23)(22,24));