Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2104 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#11318 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #401 |
| commutator | C24 | C22×C4×C19 |
| Frattini, cosocle | C25 | C23×C19 |
| prime radical | C25×C19 | C23 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C25×C19 ◁ G | |
782 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25)(26,29,33,37)(27,34)(28,31)(30,35)(32,36,39,38);(20,21)(22,23)(24,26)(25,29,31,37)(27,32,35,39)(28,33)(30,38)(34,36);(21,23)(24,27)(25,30,31,34)(26,32,33,39)(28,35)(29,36)(37,38)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4306);