Finite Group Databasebeta

?

← Prev (#492996) Next (#492998) →

C₂×#12623 #492997

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

Aliases

Subgroups

1272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4,8,13,9,6,11,20)(5,14,17,31,18,28,25,34)(7,12,22,29,23,19,27,33)(10,24,26,21,15,30,32,16);(3,5)(4,10)(6,15)(7,21,23,16)(8,17)(9,18)(11,25)(12,28,19,14)(13,26)(20,32)(22,30,27,24)(29,34,33,31);(3,6,8,20,9,4,11,13)(5,15,17,32,18,10,25,26)(7,19,22,33,23,12,27,29)(14,30,31,16,28,24,34,21)

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, 400193);