Finite Group Databasebeta

?

← Prev (#353125) Next (#353127) →

C₂×#10699 #353126

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

Aliases

Subgroups

2466 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)(9,19,22,29)(10,15)(11,16)(12,18)(13,17)(14,21,28,23)(20,33,35,38)(24,30)(25,32)(26,31)(27,34,37,36);(4,6)(7,9)(8,14,17,28)(10,20)(11,21)(12,23)(13,22)(15,27,31,37)(16,19,18,29)(24,34)(25,36)(26,35)(30,33,32,38);(7,10,12,25,13,26,11,24)(8,15,18,32,17,31,16,30)(9,20,23,36,22,35,21,34)(14,27,29,38,28,37,19,33)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260322);