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C₂²×#46384 #72296033

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

Aliases

Subgroups

90661 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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