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C₂×#32700 #7513945

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

Aliases

Subgroups

2282 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7421141);