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C₂²×#3339 #10576571

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

Aliases

Subgroups

7254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483767);