Finite Group Databasebeta

?

← Prev (#7635151) Next (#7635153) →

C₂×#37901 #7635152

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

Aliases

Subgroups

6726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,7,8)(5,9,10,6)(11,12,15,17)(13,14,16,18)(20,23)(24,26);(4,8)(6,9)(11,13)(12,14)(15,16)(17,18);(11,14)(12,16)(13,17)(15,18)(19,20)(21,24)(22,23)(25,26);(3,5)(4,6)(7,10)(8,9)(19,21,22,25)(20,24,23,26);(3,6)(4,5)(7,9)(8,10)(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, 7542348);