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C₄×#2145 #493065

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

Aliases

Subgroups

1208 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400261);