Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1347 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#7275 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | #102 |
| commutator | C2×C8 | C42×C19 |
| Frattini, cosocle | C2×C4×C8 | C22×C19 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
246 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 2 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)(27,30)(29,31)(32,33,36,40)(34,35,42,44)(37,39,45,47)(38,46,43,41);(25,28)(26,31)(29,30)(32,34,37,41,38,39,44,40,36,42,45,46,43,47,35,33)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 263);