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C₂×#10034 #232744

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

Aliases

Subgroups

1644 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

(1,2);(4,8)(5,6)(9,10)(11,12)(13,19)(14,22)(15,18)(16,21)(17,24)(20,26)(23,25);(3,4,7,10)(5,9,6,8)(16,25)(19,26);(4,8)(5,6)(9,10)(11,13)(12,16)(14,23)(15,20)(17,26)(18,25)(19,22)(21,24)

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, 139940);