Finite Group Databasebeta

?

← Prev (#10576253) Next (#10576255) →

C₂²×#3319 #10576254

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

Aliases

Subgroups

8670 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)(13,14,18,21)(15,19,17,26)(16,23,25,27)(20,24,28,22);(5,7)(6,9)(8,12)(10,11)(13,15,18,17)(14,19,21,26)(16,24,25,22)(20,23,28,27);(13,16)(14,20)(15,22)(17,24)(18,25)(19,27)(21,28)(23,26);(7,12)(9,11)(13,15,18,17)(14,19,21,26)(16,22,25,24)(20,27,28,23)

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, 10483450);