Finite Group Databasebeta

?

← Prev (#10575265) Next (#10575267) →

C₂²×#3162 #10575266

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

Aliases

Subgroups

6954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482462);