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C₂×#13310 #498815

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

Aliases

Subgroups

1584 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

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, 406011);