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C₂×#23908 #6437436

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

Aliases

Subgroups

6522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6344632);