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C₂²×#1514 #6343326

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

Aliases

Subgroups

4506 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6250522);