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C₂×#13417 #499089

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

Aliases

Subgroups

1254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406285);