Finite Group Databasebeta

?

← Prev (#7622931) Next (#7622933) →

C₂×#33589 #7622932

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

Aliases

Subgroups

2158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530128);