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C₂×#33531 #7622834

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

Aliases

Subgroups

3930 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530030);