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C₂²×#2234 #7623031

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

Aliases

Subgroups

1870 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)(14,18)(15,21)(17,24)(19,27)(20,23)(22,28)(25,26);(6,9)(10,12)(13,14,16,18)(15,19,22,26)(17,20,23,24)(21,25,28,27);(5,7,8,11)(6,10,9,12)(13,15,16,22)(14,19,18,26)(17,25,23,27)(20,28,24,21)

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, 7530227);