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C₂×#11277 #358290

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

Aliases

Subgroups

1654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265486);