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C₂×#13340 #498862

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

Aliases

Subgroups

1572 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406058);