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C₂²×#2977 #10574277

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

Aliases

Subgroups

8822 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 28 points:

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481473);