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C₂²×#1533 #6343776

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

Aliases

Subgroups

4658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6250972);