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C₂×#17382 #6342595

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

Aliases

Subgroups

3346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6249791);