Finite Group Databasebeta

?

← Prev (#6461391) Next (#6461393) →

C₂×#29233 #6461392

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

Aliases

Subgroups

1442 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6368588);