Finite Group Databasebeta

?

← Prev (#60446) Next (#60448) →

C₂×#3059 #60447

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

Aliases

Subgroups

1339 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

(1,2);(3,4)(5,6)(7,8,12,16)(9,17,21,31)(10,14,22,28)(11,24,18,15)(13,25,27,20)(19,30,33,38)(23,35,32,29)(26,36,37,34);(7,9,18,25,12,21,11,20)(8,13,24,31,16,27,15,17)(10,19,32,36,22,33,23,34)(14,26,35,38,28,37,29,30);(4,6)(7,10)(8,14)(9,19)(11,23)(12,22)(13,26)(15,29)(16,28)(17,30)(18,32)(20,34)(21,33)(24,35)(25,36)(27,37)(31,38);(10,22)(14,28)(19,33)(23,32)(26,37)(29,35)(30,38)(34,36)

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, 53435);