Finite Group Databasebeta

?

← Prev (#7622606) Next (#7622608) →

C₂×#33457 #7622607

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

Aliases

Subgroups

2018 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,6,5)(7,8)(9,17)(10,21)(11,26)(12,14)(13,18)(15,24)(16,23)(19,37)(20,34)(22,32)(25,33)(27,31)(28,36)(29,38)(30,35);(7,9,12,20)(8,13,14,28)(10,22,25,38)(11,27,23,19)(15,31,30,37)(16,32,26,29)(17,33,34,21)(18,35,36,24);(3,5,6,4)(7,8)(9,13)(10,15)(11,16)(12,14)(17,18)(19,29)(20,28)(21,24)(22,31)(23,26)(25,30)(27,32)(33,35)(34,36)(37,38);(8,14)(13,28)(15,30)(16,26)(17,34)(21,33)(29,32)(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, 7529803);