Finite Group Databasebeta

?

← Prev (#6437598) Next (#6437600) →

C₂×#23889 #6437599

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

Aliases

Subgroups

5983 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)(9,19)(10,24)(11,18)(12,17)(13,22)(14,26)(15,25)(16,29)(20,35)(21,30)(23,32)(27,34)(28,31)(33,37)(36,38);(7,9,12,23)(8,13,17,31)(10,21,26,36)(11,28,29,22)(14,33,24,35)(15,30,34,38)(16,32,18,19)(20,25,37,27);(4,6)(7,10)(8,14)(9,20)(11,25)(12,26)(13,30)(15,16)(17,24)(18,34)(19,33)(21,28)(22,36)(23,37)(27,29)(31,38)(32,35);(7,10)(8,15)(9,21)(11,27)(12,26)(13,30)(14,16)(17,34)(18,24)(19,35)(20,28)(22,37)(23,36)(25,29)(31,38)(32,33)

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344795);