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C₂×#17892 #6344584

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

Aliases

Subgroups

1864 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6251780);