Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#23367 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle, prime radical | C23×C19 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
600 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26)(23,25)(24,27)(28,29)(30,37)(31,35)(32,41)(33,36)(34,40)(38,43)(39,42)(44,45,47,50,48,51,54,57)(46,49,53,56,52,55,58,59);(22,27)(24,26)(28,30,33,40)(29,34,36,37)(31,39,32,38)(35,43,41,42);(20,22,23,27)(21,24,25,26)(28,31,33,32)(29,35,36,41)(30,38,40,39)(34,42,37,43)(44,46)(45,49)(47,53)(48,52)(50,56)(51,55)(54,58)(57,59);(21,25)(24,26)(28,32,33,31)(29,35,36,41)(30,39,40,38)(34,42,37,43)(46,52)(49,55)(53,58)(56,59)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16355);