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C₂×#22456 #6379182

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

Aliases

Subgroups

4610 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6286378);