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C₂²×#1653 #6348043

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

Aliases

Subgroups

3086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6255239);