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C₂×#18528 #6348072

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

Aliases

Subgroups

3480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 6255268);