Finite Group Databasebeta

?

← Prev (#7623672) Next (#7623674) →

C₂×#33863 #7623673

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

Aliases

Subgroups

1622 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 42 points:

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530869);