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C₂×#23434 #6431776

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

Aliases

Subgroups

7122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6338972);