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C₂²×#1389 #492880

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

Aliases

Subgroups

1658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 36 points:

(1,2);(3,4);(5,6,9,14,11,15,10,26)(7,16,18,33,21,29,20,35)(8,22,23,31,25,36,24,13)(12,27,28,19,30,34,32,17);(5,7,8,19,9,18,23,34,11,21,25,17,10,20,24,27)(6,12,13,29,26,32,36,33,15,30,31,16,14,28,22,35)

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, 400076);