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C₂×#3042 #60417

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

Aliases

Subgroups

1441 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(7,8,11,15)(9,12,16,20)(10,13,18,14)(17,19,22,21);(3,4,5,6)(7,9)(8,12)(10,17)(11,16)(13,19)(14,21)(15,20)(18,22);(8,13)(10,18)(12,19)(14,15)(17,22)(20,21);(9,16)(12,20)(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, 53405);