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C₂²×#15463 #72293262

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

Aliases

Subgroups

69197 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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