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C₂²×#16557 #72334494

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

Aliases

Subgroups

77085 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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