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C₄×#473 #21554

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

Aliases

Subgroups

441 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14542);