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C₂²×#1643 #6348025

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

Aliases

Subgroups

3346 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)(16,21,17,20)(19,25,28,24);(5,6,8,10)(7,12,11,9)(13,15,18,26)(14,19,22,28)(16,25,17,24)(20,27,21,23);(14,20)(16,17)(19,27)(21,22)(23,28)(24,25)

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, 6255221);