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C₂×#33568 #7622898

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

Aliases

Subgroups

3750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530094);