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C₂×#13079 #494670

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

Aliases

Subgroups

1362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401866);