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C₂×#33554 #7622865

• p-group
• nilpotent
• supersolvable
• solvable
• monomial
• rational
• ambivalent

Aliases

Subgroups

3743 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530061);