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C₂×#13373 #498967

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

Aliases

Subgroups

956 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406163);