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C₂×#33690 #7623146

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

Aliases

Subgroups

1505 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530342);