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C₂×#33553 #7622864

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

Aliases

Subgroups

4207 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530060);