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C₂×#19181 #6353656

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

Aliases

Subgroups

1690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6260852);