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C₂×#33569 #7622899

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

Aliases

Subgroups

3664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530095);