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C₂×#43904 #7668121

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

Aliases

Subgroups

12742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7575317);