Finite Group Databasebeta

?

← Prev (#72296607) Next (#72296609) →

C₂²×#40728 #72296608

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

Aliases

Subgroups

93913 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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