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C₂×#13033 #494551

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

Aliases

Subgroups

1394 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401747);