Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#34342 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| socle | C23×C19 | C25 |
| prime radical | C2×C19×#525 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
2474 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(24,25)(26,28)(27,29)(30,31)(32,33)(34,40)(35,39)(36,38)(37,41)(42,46)(43,45)(44,47);(24,26)(25,28)(27,30)(29,31)(32,34)(33,37)(35,42)(36,41)(38,40)(39,44)(43,47)(45,46);(25,29)(26,30)(34,41)(37,40)(42,47)(44,46);(25,29)(28,31)(33,38)(34,41)(39,45)(42,47);(32,35,36,43)(33,39,38,45)(34,42,41,47)(37,44,40,46)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27330);