Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C19 · Schur multiplier (H2) = C9 |
| direct product | C19×#6898 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C19 | C33 |
| commutator, Frattini, cosocle | C32 | C33×C19 |
| prime radical | C33×C19 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C19 ◁ G | |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 1539 |
A minimal faithful permutation representation — 3 generators on 73 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24)(22,26,32)(23,27,31)(25,33,30)(28,35,40)(29,36,39)(34,41,38)(37,43,45)(42,46,44)(47,48,51)(49,52,58)(50,54,59)(53,63,57)(55,60,66)(56,62,67)(61,70,65)(64,69,72)(68,73,71);(21,25,27)(24,31,33)(26,34,36)(32,39,41)(35,42,43)(40,45,46)(47,49,55,50,56,64,57,65,71)(48,52,60,54,62,69,53,61,68)(51,58,66,59,67,72,63,70,73);(20,22,28,30,38,44,23,29,37)(21,26,35,25,34,42,27,36,43)(24,32,40,33,41,46,31,39,45)(48,53,54)(51,59,63)(52,61,62)(58,67,70)(60,68,69)(66,72,73)969 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 45);