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C₄×#563 #34354

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

Aliases

Subgroups

1012 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 28 points:

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27342);