Finite Group Databasebeta

?

← Prev (#7638713) Next (#7638715) →

C₂×#40812 #7638714

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

Aliases

Subgroups

6342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7545910);