Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #6909 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C19 · Schur multiplier (H2) = C33 |
| direct product | C19×#6913 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C19 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C32 | C33×C19 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C19 ◁ C3×C9×C19 ◁ G | |
126 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 513 |
A minimal faithful permutation representation — 3 generators on 46 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24)(22,26,31)(23,25,32)(27,36,30)(28,33,40)(29,35,41)(34,43,37)(38,42,45)(39,44,46);(21,25,27)(22,28,37)(26,34,33)(29,39,38)(31,40,43)(41,46,45);(20,22,29,23,28,38,30,37,39)(21,26,35,25,33,42,27,34,44)(24,31,41,32,40,45,36,43,46)665 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 60);