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C₂×#23834 #6432672

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

Aliases

Subgroups

1714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339868);