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C₂×#10756 #353451

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

Aliases

Subgroups

4094 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260647);