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C₂×#11540 #480372

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

Aliases

Subgroups

668 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 387568);