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C₂²×#15203 #72334498

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

Aliases

Subgroups

76725 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 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((6,7)(10,12)(13,14)(15,18)(16,17)(19,20)(21,22,24,25)(23,27,28,26), (10,12)(14,17)(15,19)(22,25)(23,28), (5,6,8,7)(9,10)(11,12)(13,14)(15,20)(16,17)(18,19)(21,23,24,28)(22,26,25,27), (5,7,8,6)(9,10)(11,12)(13,15,16,19)(14,18,17,20)(21,22)(23,26)(24,25)(27,28), (3,4), (1,2)(3,4));