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C₂×#19950 #6358322

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

Aliases

Subgroups

1606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6265518);