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C₂×#23833 #6432671

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

Aliases

Subgroups

1736 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)(16,28,30,34)(19,25)(20,32)(21,26)(23,31,33,29);(5,15,17,18)(10,14,24,27)(16,29,30,31)(23,28,33,34);(3,5)(4,10)(6,16)(7,15)(8,18)(9,17)(11,23)(12,27)(13,24)(14,22)(19,29)(20,31)(21,30)(25,34)(26,33)(28,32);(3,6,7,19,9,21,8,20)(4,11,12,25,13,26,22,32)(5,16,15,29,17,30,18,31)(10,23,27,34,24,33,14,28)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339867);