Finite Group Databasebeta

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C₂²×#7708420 #72335819

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

Aliases

Subgroups

At least 6849 conjugacy classes of subgroups; only the 445912 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);(5,6,7,8)(11,15)(14,16)(17,19,21,24)(18,22,20,23);(10,13)(14,16)(17,19)(18,23)(20,22)(21,24);(5,6,7,8)(9,10)(11,16)(12,13)(14,15)(17,20,21,18)(19,23,24,22);(3,4);(5,6)(7,8)(17,19)(18,23)(20,22)(21,24);(1,2)(3,4);(9,11)(10,14)(12,15)(13,16)

Conjugacy classes & character table

416 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), (5,6,7,8)(11,15)(14,16)(17,19,21,24)(18,22,20,23), (10,13)(14,16)(17,19)(18,23)(20,22)(21,24), (5,6,7,8)(9,10)(11,16)(12,13)(14,15)(17,20,21,18)(19,23,24,22), (3,4), (5,6)(7,8)(17,19)(18,23)(20,22)(21,24), (1,2)(3,4), (9,11)(10,14)(12,15)(13,16));