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C₂×#33348 #7622446

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

Aliases

Subgroups

4992 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529642);