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C₂×#33428 #7622562

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

Aliases

Subgroups

1512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7529758);