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C₂×#33570 #7622900

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

Aliases

Subgroups

4101 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 18 points:

(1,2);(3,4)(5,11)(6,9)(7,10)(8,13)(12,16)(14,18)(15,17);(4,9)(5,6)(7,16)(10,17)(11,13)(12,18);(4,10)(7,16)(9,17)(11,18)(12,13)(14,15);(3,5,8,6)(4,11,13,9)(7,14,16,15)(10,18,12,17)

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, 7530096);