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C₂²×#2153 #7622522

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

Aliases

Subgroups

2090 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 36 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529718);