Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#8227 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C2×C22⋊C4 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C43×C19 ◁ G | |
488 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22)(24,25)(26,28)(27,30)(29,31)(32,33,35,38)(34,40,41,37)(36,44,43,39)(42,45,47,46);(25,28,30,29)(32,34,36,42,35,41,43,47)(33,37,39,45,38,40,44,46);(20,22,23,21)(34,41)(37,40)(42,47)(45,46)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1215);