Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11247 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#11277 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #387 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1442 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
592 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,30,33,26)(23,34)(24,29)(25,28)(27,36)(31,40,48,46)(32,47,50,41)(35,42,49,51)(37,45)(38,43)(39,44);(20,22)(21,26)(23,35,36,49)(24,32)(25,33)(27,42,34,51)(28,30)(29,41)(31,37,48,38)(39,50)(40,43,46,45)(44,47);(20,23)(21,27,28,34)(22,31)(24,38)(25,36)(26,40,30,46)(29,45,44,43)(32,49)(33,48)(35,50)(37,39)(41,51,47,42)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4265);