Finite Group Databasebeta

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C₂²×#7718061 #72336350

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

Aliases

Subgroups

At least 6033 conjugacy classes of subgroups; only the 445480 normal subgroups are shown.

Full subgroup data →

Presentation

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

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