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C₂²×#3333823 #72296972

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

Aliases

Subgroups

At least 6960 conjugacy classes of subgroups; only the 35776 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 32 points:

(6,8)(18,19)(22,23)(27,31)(30,32);(5,6,7,8)(11,15)(14,16)(17,18,21,19)(20,23,24,22)(25,26,28,29)(27,30,31,32);(5,6,7,8)(10,13)(11,15)(18,19)(20,24)(26,29)(30,32);(5,6,7,8)(9,10)(11,16)(12,13)(14,15)(17,19,21,18)(20,22,24,23)(25,27,28,31)(26,30,29,32);(5,6)(7,8)(9,11)(10,14)(12,15)(13,16)(17,20)(18,22)(19,23)(21,24)(25,26)(27,32)(28,29)(30,31);(3,4);(1,2)(3,4)

Conjugacy classes & character table

296 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)(18,19)(22,23)(27,31)(30,32), (5,6,7,8)(11,15)(14,16)(17,18,21,19)(20,23,24,22)(25,26,28,29)(27,30,31,32), (5,6,7,8)(10,13)(11,15)(18,19)(20,24)(26,29)(30,32), (5,6,7,8)(9,10)(11,16)(12,13)(14,15)(17,19,21,18)(20,22,24,23)(25,27,28,31)(26,30,29,32), (5,6)(7,8)(9,11)(10,14)(12,15)(13,16)(17,20)(18,22)(19,23)(21,24)(25,26)(27,32)(28,29)(30,31), (3,4), (1,2)(3,4));