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C₂×#12799 #493708

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

Aliases

Subgroups

1634 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400904);