Finite Group Databasebeta

?

← Prev (#6371393) Next (#6371395) →

C₂×#20917 #6371394

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

Aliases

Subgroups

6170 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278590);