Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#13277 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C2×D8 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
366 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)(21,23)(24,25)(26,30)(27,28)(29,31)(32,33,36,41,44,47,43,38,35,39,34,40,37,42,45,46);(20,21,22,23)(25,28)(29,30)(33,38)(34,43)(36,45)(37,44)(39,46)(40,42)(41,47);(24,26,27,31)(25,29,28,30)(33,39)(38,46)(40,41)(42,47)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6265);