Finite Group Databasebeta

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C₂²×#7966197 #72336758

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

Aliases

Subgroups

At least 16815 conjugacy classes of subgroups; only the 445696 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

404 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)(11,12)(13,15)(14,16)(17,18,20,22)(19,21,23,24), (6,8)(9,11)(10,14)(12,15)(13,16)(19,23)(21,24), (9,10)(11,14)(12,16)(13,15)(17,18)(19,24)(20,22)(21,23), (6,8)(10,15)(12,14)(17,18)(19,24)(20,22)(21,23), (3,4), (6,8)(9,11)(10,14)(12,15)(13,16)(17,18)(19,24)(20,22)(21,23), (1,2)(3,4), (5,6)(7,8)(9,12,13,14)(10,16,15,11)(17,19)(18,21)(20,23)(22,24));