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C₂×#36429 #7630109

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

Aliases

Subgroups

25052 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537305);