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C₂²×#3210 #10575483

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

Aliases

Subgroups

8110 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)(13,14,18,21)(15,22,24,27)(16,20,17,25)(19,26,28,23);(5,7,8,12)(6,9,10,11);(7,12)(9,11)(13,15)(14,19)(16,23)(17,26)(18,24)(20,27)(21,28)(22,25);(6,10)(9,11)(13,16,18,17)(14,20,21,25)(15,23,24,26)(19,27,28,22)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482679);