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C₂²×#1506 #6343295

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

Aliases

Subgroups

3714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 28 points:

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

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, 6250491);