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C₂²×#62987 #72278398

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

Aliases

Subgroups

841225 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

340 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((9,10)(11,13)(12,19)(14,16)(15,22)(17,24)(18,23)(20,21), (9,10,14,16)(11,13,18,23)(12,19,22,15)(17,24,20,21), (6,8)(9,11,14,18)(10,13,16,23)(12,17,22,20)(15,21,19,24), (5,6)(7,8)(9,11)(10,13)(12,20)(14,18)(15,24)(16,23)(17,22)(19,21), (9,12)(10,15)(11,17)(13,21)(14,22)(16,19)(18,20)(23,24), (9,13)(10,11)(12,21)(14,23)(15,17)(16,18)(19,20)(22,24), (3,4), (1,2)(3,4));