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C₂×#3009 #60361

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

Aliases

Subgroups

2531 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)(9,13,16,20)(10,12,18,14)(17,19,22,21);(8,12)(10,18)(13,19)(14,15)(17,22)(20,21);(4,6)(7,9)(8,13)(10,17)(11,16)(12,19)(14,21)(15,20)(18,22);(9,16)(13,20)(17,22)(19,21)

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53349);