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C₂×#23899 #6437462

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

Aliases

Subgroups

6040 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6344658);