Finite Group Databasebeta

?

← Prev (#20618) Next (#20620) →

C₂×#1794 #20619

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

Aliases

Subgroups

1831 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 13607);