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C₂×#13404 #499041

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

Aliases

Subgroups

1106 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)(7,21)(11,27)(12,22)(13,19)(15,30)(16,23)(17,32)(18,31)(20,24)(25,29)(28,33);(3,4)(5,15)(6,19)(7,22)(8,10)(9,13)(11,17)(12,24)(14,29)(16,28)(18,25)(20,26)(21,34)(23,30)(27,31)(32,33);(3,5)(4,11,13,15)(6,18)(7,23)(8,16)(9,17)(10,25,19,28)(12,30,22,27)(14,21)(20,32)(24,31)(26,29,34,33)

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, 406237);