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C₂×#12806 #493732

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

Aliases

Subgroups

1132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400928);