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C₂×#25179 #6438648

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

Aliases

Subgroups

3800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6345844);