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C₂×#12982 #494417

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

Aliases

Subgroups

1320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401613);