Finite Group Databasebeta

?

← Prev (#10586177) Next (#10586179) →

C₂×#62830 #10586178

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

Aliases

Subgroups

35128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493374);