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C₂×#13070 #494652

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

Aliases

Subgroups

1274 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401848);