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C₂×#13389 #499023

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

Aliases

Subgroups

1098 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406219);