Finite Group Databasebeta

?

← Prev (#7637777) Next (#7637779) →

C₂×#40168 #7637778

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

Aliases

Subgroups

6004 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7544974);