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C₅×#6879 #11925952

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1215, 26);