Finite Group Databasebeta

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C₂²×#7850713 #72301211

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

Aliases

Subgroups

At least 10536 conjugacy classes of subgroups; only the 445520 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

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