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C₂²×#48454 #72291772

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

Aliases

Subgroups

83789 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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