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C₂×#33561 #7622873

• p-group
• nilpotent
• supersolvable
• solvable
• monomial
• rational
• ambivalent

Aliases

Subgroups

3693 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530069);