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Aliases
Splittings
Subgroups
40 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 53 points:
(1,3,7,9,4)(2,10,8,15,14,11,12,5,6,13)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(46,48)(47,51)(49,50)(52,53);(1,2,5)(3,6,11)(4,8,13)(7,12,15)(9,14,10)(16,17,19,21,23,25,27,29,31,33,35,37,39,41,43,44,42,40,38,36,34,32,30,28,26,24,22,20,18)(45,53,48,51,50,49,47,46,52)
Polycyclic presentation:
2,3,29,5^2,3|b^3=f^2,b^a=b^2f,c^a=c^28,d^a=d^2e,e^a=d^2e^3,f^a=f^2,d^b=d^2e^4,e^b=d^2e^2
Conjugacy classes & character table
486 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13050, 23);
Finite Group Databasebeta