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C₂×#18216 #6346487

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

Aliases

Subgroups

3188 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6253683);