Finite Group Databasebeta

?

← Prev (#6437618) Next (#6437620) →

C₂×#23905 #6437619

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

Aliases

Subgroups

6244 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344815);