Finite Group Databasebeta

?

← Prev (#7702568) Next (#7702570) →

C₂×#46089 #7702569

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

Aliases

Subgroups

9198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7609765);