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C₂²×#2228 #7622997

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

Aliases

Subgroups

1762 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530193);