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C₂×#23472 #6431842

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

Aliases

Subgroups

3858 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339038);