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C₂²×#55040 #72296605

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

Aliases

Subgroups

89829 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 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((13,14)(15,18)(16,17)(19,20)(21,22)(23,27)(24,26)(25,28), (7,11)(10,12)(14,17)(18,19)(21,22)(23,25)(24,26)(27,28), (6,9)(7,11)(13,15)(14,18)(16,20)(17,19)(21,22,24,26)(23,25,28,27), (5,6)(7,12)(8,9)(10,11)(13,15)(14,18)(16,20)(17,19)(21,22)(23,25)(24,26)(27,28), (5,7)(6,10)(8,11)(9,12)(13,14)(15,19)(16,17)(18,20)(21,23)(22,25)(24,28)(26,27), (3,4), (1,2)(3,4));