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C₂×#19315 #6353973

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

Aliases

Subgroups

1712 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6261169);