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C₂×#20606 #6370727

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

Aliases

Subgroups

17390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

(1,2);(3,4)(5,6)(7,8,11,15,12,9,16,14)(10,13,19,21,18,17,22,20);(7,9)(8,12)(10,17)(11,14)(13,18)(15,16)(19,20)(21,22);(4,6)(7,10)(8,13)(9,17)(11,19)(12,18)(14,20)(15,21)(16,22);(10,18)(13,17)(19,22)(20,21)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6277923);