Finite Group Databasebeta

?

← Prev (#7626199) Next (#7626201) →

C₄×#3550 #7626200

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

Aliases

Subgroups

6976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7533396);