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C₄×#2736 #521278

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

Aliases

Subgroups

3546 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 428474);