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C₂×#18088 #6345132

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

Aliases

Subgroups

1704 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6252328);