Finite Group Databasebeta

?

← Prev (#492916) Next (#492918) →

C₂×#12593 #492917

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

Aliases

Subgroups

818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 42 points:

(1,2);(3,4)(5,8)(6,7)(9,10)(11,12,16,22,17,24,32,39,18,23,31,38,15,21,14,20)(13,25,28,41,29,19,26,35,30,37,33,34,27,36,42,40);(4,7)(8,10)(11,13)(12,19,23,36)(14,26)(15,27)(16,33)(17,29)(18,30)(20,34,39,41)(21,25,24,37)(22,40,38,35)(28,31)(32,42);(3,5,6,9)(4,8,7,10)(11,14,15,31,18,32,17,16)(12,20,21,38,23,39,24,22)(13,26,27,28,30,42,29,33)(19,34,25,35,36,41,37,40)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400113);