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C₄×#2148 #493069

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

Aliases

Subgroups

1184 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400265);