Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #6856 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C19 · Schur multiplier (H2) = C3 |
| direct product | C19×#6859 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C19 | H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C32×C19 |
| prime radical | C3×C19×H(3,𝔽3) | C3 |
| LCS | G ▷ C33 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C19 ◁ C33×C19 ◁ G | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1539 |
A minimal faithful permutation representation — 2 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23,25)(29,30,33)(31,37,41)(32,36,42)(34,43,39)(35,46,40)(38,48,51)(44,54,55)(45,53,50)(47,52,49);(20,21,24)(22,25,28)(23,27,26)(29,31,38,40,50,55,32,39,49)(30,34,44,35,37,47,36,45,48)(33,41,51,46,53,54,42,43,52)665 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 6);