Finite Group Databasebeta

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C₂²×#38540 #72295860

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

Aliases

Subgroups

89601 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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