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C₂×#13402 #499038

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

Aliases

Subgroups

1102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406234);