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C₂×#8183 #182180

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

Aliases

Subgroups

1554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 30 points:

(1,2);(3,4,6,5)(8,12)(9,10)(13,14)(15,16,19,22)(17,23,24,30)(18,26,27,21)(20,28,29,25);(7,8,10,13,11,14,9,12)(15,17)(16,20,22,29)(18,25)(19,24)(21,23,26,30)(27,28);(3,5,6,4)(7,9,11,10)(8,12,14,13)(17,24)(20,29)(23,30)(25,28)

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 89376);