Finite Group Databasebeta

?

← Prev (#60163) Next (#60165) →

C₂×#2950 #60164

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

Aliases

Subgroups

1327 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53152);