Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2230 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#12950 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #476 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C2×C4×C8×C19 ◁ G | |
412 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1216 |
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)(20,21)(22,23)(25,31,33,26)(27,37)(28,38)(29,39)(32,34,36,35);(21,23)(24,25,29,35,30,33,39,34)(26,27,32,37,31,38,36,28);(24,26)(25,27)(28,34)(29,32)(30,31)(33,38)(35,37)(36,39)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5938);