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C₂×#31177 #7503609

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

Aliases

Subgroups

2438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7410805);