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C₂×#12633 #493025

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

Aliases

Subgroups

1234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

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, 400221);