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C₂×#58999 #7666019

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

Aliases

Subgroups

12484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 18 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573215);