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C₂²×#44241 #72293735

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

Aliases

Subgroups

87873 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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((7,11)(10,12)(13,14)(15,19)(16,18)(17,20)(21,22,25,27)(23,26,28,24), (6,9)(10,12)(13,14,16,18)(15,17,20,19)(21,23,25,28)(22,26,27,24), (15,20)(17,19)(22,27)(23,28), (5,6)(7,12)(8,9)(10,11)(13,14)(15,19)(16,18)(17,20)(21,23)(22,26)(24,27)(25,28), (5,7,8,11)(6,10,9,12)(13,15,16,20)(14,17,18,19)(21,24,25,26)(22,28,27,23), (3,4), (1,2)(3,4));