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C₂×#18792 #6348709

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

Aliases

Subgroups

3478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6255905);