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C₂²×#1812 #6370823

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

Aliases

Subgroups

4658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278019);