Finite Group Databasebeta

?

← Prev (#10576683) Next (#10576685) →

C₂²×#3401 #10576684

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

Aliases

Subgroups

7274 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 28 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483880);