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C₂×#20193 #6359545

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

Aliases

Subgroups

1947 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6266741);