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C₂×#11539 #480371

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

Aliases

Subgroups

690 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)(5,15,17,32,18,28,33,30,19,24,22,34,16,11,26,27);(4,10,14,12)(7,21)(11,24,28,15)(13,25,31,29)(17,22)(20,23)(26,33)(27,34,30,32);(3,5,8,18,9,19,6,16)(4,11,10,24,14,28,12,15)(7,22,23,26,21,17,20,33)(13,30,25,32,31,27,29,34)

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, 387567);