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C₂²×#14341 #72339131

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

Aliases

Subgroups

166005 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 28 points:

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

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((13,14)(15,18)(16,17)(19,20)(22,25)(26,27), (6,8)(10,12)(14,17)(18,19)(21,22,24,25)(23,26,28,27), (5,6)(7,8)(9,10,11,12)(13,14)(15,19)(16,17)(18,20)(21,22)(23,27)(24,25)(26,28), (3,4), (1,2)(3,4), (13,15)(14,18)(16,20)(17,19)(21,23)(22,26)(24,28)(25,27));