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C₂×#33426 #7622560

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

Aliases

Subgroups

1490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529756);