Finite Group Databasebeta

?

← Prev (#7500759) Next (#7500761) →

C₂×#30442 #7500760

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

Aliases

Subgroups

2733 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7407956);