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C₂×#12792 #493686

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

Aliases

Subgroups

1208 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400882);