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C₄×#2263 #512762

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

Aliases

Subgroups

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 419958);