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C₂²×#48088 #72293722

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

Aliases

Subgroups

92185 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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