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C₂×#13512 #499415

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

Aliases

Subgroups

538 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406611);