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C₂×#20136 #6359469

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

Aliases

Subgroups

1682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6266665);