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C₄×#541 #34095

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

Aliases

Subgroups

1035 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)(15,21,22,18)(16,24,25,19)(23,26,28,27);(5,7,8,11)(6,9,10,12)(13,15)(14,18)(16,23)(17,22)(19,26)(20,21)(24,27)(25,28);(6,10)(9,12)(15,22)(18,21)(23,28)(26,27);(13,16,17,25)(14,19,20,24)(15,23,22,28)(18,26,21,27)

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27083);