Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#8287 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C2×D4 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| socle, prime radical | C23×C19 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ C2×C4×C8×C19 ◁ G | |
398 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 4864 |
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)(24,25,27,29,28,31,26,30)(32,33,36,38,35,37,39,34);(20,21,22,23)(25,29)(26,27)(30,31)(33,37)(34,38);(24,26,28,27)(25,29,31,30)(32,34,39,37,35,38,36,33)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1275);