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C₂×#7936 #181097

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

Aliases

Subgroups

1546 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)(19,20,23,26,24,27,22,31)(21,28,29,33,30,25,32,34);(3,5,7,16,8,15,6,14)(4,9,12,18,11,13,10,17)(19,21)(20,25)(22,29)(23,32)(24,30)(26,33)(27,28)(31,34);(3,6,8,7)(4,10,11,12)(5,14,15,16)(9,17,13,18)(19,22,24,23)(20,26,27,31)(21,29,30,32)(25,33,28,34)

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, 88293);