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C₂²×#3561 #10586131

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

Aliases

Subgroups

35226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10493327);