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C₂²×#3554 #10586146

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

Aliases

Subgroups

34862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 28 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493342);