Finite Group Databasebeta

?

← Prev (#7635955) Next (#7635957) →

C₂×#38510 #7635956

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

Aliases

Subgroups

8718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7543152);