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C₂×#12968 #494377

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

Aliases

Subgroups

1113 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401573);