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C₂²×#1641 #6348054

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

Aliases

Subgroups

4462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 28 points:

(1,2);(3,4);(5,6)(7,9)(8,11)(10,12)(13,14,17,20)(15,21,22,28)(16,24,25,19)(18,26,27,23);(6,9)(7,12)(10,11)(16,25)(19,24)(21,28)(23,26);(13,15,17,22)(14,18,20,27)(16,26,25,23)(19,28,24,21)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6255250);