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C₄×#2123 #492993

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

Aliases

Subgroups

1267 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400189);