Finite Group Databasebeta

?

← Prev (#7513945) Next (#7513947) →

C₂×#32701 #7513946

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

Aliases

Subgroups

1742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7421142);