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C₅⋊#564 #66020

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

172 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 37 points:

(1,2,4,5,3)(7,13)(11,19)(12,21)(18,20)(22,25,26,33)(23,29,28,36)(24,31,30,32)(27,34,35,37);(6,9,10,17)(7,12,13,21)(8,14,15,16)(11,18,19,20)(23,28)(24,30)(29,36)(31,32);(6,8,10,15)(7,11,13,19)(9,16,17,14)(12,20,21,18)(22,24)(23,27)(25,32)(26,30)(28,35)(29,37)(31,33)(34,36);(2,3)(4,5)(6,7)(8,11)(9,12)(10,13)(14,18)(15,19)(16,20)(17,21)(22,23,26,28)(24,27,30,35)(25,29,33,36)(31,34,32,37)

Polycyclic presentation:

2^6,5|a^2=f,b^2=e,c^2=e,d^2=f,c^a=cf,d^a=de,g^a=g^4,c^b=cef,d^b=df

Conjugacy classes & character table

47 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 1358);