Finite Group Databasebeta

?

← Prev (#7667152) Next (#7667154) →

C₂×#43055 #7667153

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

Aliases

Subgroups

6582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7574349);