Finite Group Databasebeta

?

← Prev (#61100) Next (#61102) →

C₂×#3290 #61101

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

Aliases

Subgroups

1325 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54089);