Finite Group Databasebeta

?

← Prev (#7629348) Next (#7629350) →

C₂×#35894 #7629349

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

Aliases

Subgroups

6546 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536545);