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C₂×#12828 #493795

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

Aliases

Subgroups

1050 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400991);