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C₂²×#1814 #6370827

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

Aliases

Subgroups

4618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278023);