Finite Group Databasebeta

?

← Prev (#60791) Next (#60793) →

C₂×#3222 #60792

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

Aliases

Subgroups

1107 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53780);