Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#8179 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C2×D4 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| socle | C23×C19 | C2×C22⋊C4 |
| prime radical | C22×D4×C19 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ C43×C19 ◁ G | |
562 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2432 |
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)(25,29)(26,27)(30,31)(32,33,36,39)(34,40,41,47)(35,43,44,38)(37,45,46,42);(24,25,27,30,28,31,26,29)(32,34)(33,37,39,46)(35,42)(36,41)(38,40,43,47)(44,45);(20,22,23,21)(24,26,28,27)(25,30,31,29)(34,41)(37,46)(40,47)(42,45)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1167);