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C₂×#12716 #493417

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

Aliases

Subgroups

3386 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400613);