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C₂×#33556 #7622867

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

Aliases

Subgroups

3807 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)(16,29)(18,30)(19,25)(20,34)(21,27)(22,28)(23,31)(24,33)(26,32);(3,5,9,18)(4,10,14,24)(6,16,7,20)(8,17,22,33)(11,23,12,26)(13,15,28,30)(19,31,21,32)(25,29,27,34);(3,6,9,7)(4,11,14,12)(5,16,18,20)(8,21,22,19)(10,23,24,26)(13,25,28,27)(15,29,30,34)(17,32,33,31);(3,7,9,6)(4,12,14,11)(5,16,18,20)(8,21,22,19)(10,23,24,26)(13,27,28,25)(15,29,30,34)(17,31,33,32)

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, 7530063);