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C₂²×#14865 #72334493

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

Aliases

Subgroups

80181 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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