Finite Group Databasebeta

?

← Prev (#7668152) Next (#7668154) →

C₂×#44081 #7668153

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

Aliases

Subgroups

6154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7575349);