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C₄×#536 #34089

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

Aliases

Subgroups

1481 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

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, 27077);