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C₂²×#15527 #72296838

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

Aliases

Subgroups

52285 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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