Finite Group Databasebeta

?

← Prev (#354055) Next (#354057) →

C₂×#10961 #354056

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

Aliases

Subgroups

2882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261252);