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C₂×#8118 #181390

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

Aliases

Subgroups

1466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 88586);