Finite Group Databasebeta

?

← Prev (#8103973) Next (#8103975) →

C₂×#58254 #8103974

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

Aliases

Subgroups

6250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

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, 8011170);