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C₂²×#7655557 #72336256

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

Aliases

Subgroups

At least 6930 conjugacy classes of subgroups; only the 447112 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

392 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((17,18,21,20)(19,23,24,22), (5,6,8,7)(9,10,14,12)(11,15,16,13)(17,19,21,24)(18,22,20,23), (9,11)(10,15)(12,13)(14,16)(17,19)(18,23)(20,22)(21,24), (6,7)(10,12)(11,16)(17,19)(18,23)(20,22)(21,24), (3,4), (5,7,8,6)(9,12,14,10)(11,13,16,15)(17,20,21,18)(19,23,24,22), (1,2)(3,4), (9,13)(10,16)(11,12)(14,15));