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C₂×#17994 #6344893

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

Aliases

Subgroups

2198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6252089);