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C₂×#8120 #181393

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

Aliases

Subgroups

1472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 88589);