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C₂²×#1820 #6370865

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

Aliases

Subgroups

5466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278061);