Finite Group Databasebeta

?

← Prev (#7623139) Next (#7623141) →

C₂×#33691 #7623140

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

Aliases

Subgroups

1499 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530336);