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C₂²×#48555 #72293733

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

Aliases

Subgroups

83865 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 28 points:

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

Conjugacy classes & character table

208 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)(15,17)(16,18)(19,20)(21,22,25,27)(23,24,28,26), (6,9)(7,11)(13,14,16,18)(15,17,20,19)(21,23)(22,26)(24,27)(25,28), (7,11)(10,12)(22,27)(23,28), (5,6)(7,12)(8,9)(10,11)(13,14)(15,19)(16,18)(17,20)(21,23)(22,24)(25,28)(26,27), (5,7)(6,10)(8,11)(9,12)(13,15)(14,17)(16,20)(18,19)(21,24)(22,28)(23,27)(25,26), (3,4), (1,2)(3,4));