Finite Group Databasebeta

?

← Prev (#60683) Next (#60685) →

C₂×#3179 #60684

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

Aliases

Subgroups

1017 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53672);