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C₂²×#1881 #6371430

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

Aliases

Subgroups

6118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278626);