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C₂×#19273 #6353905

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

Aliases

Subgroups

1738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6261101);