Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#9731 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | #121 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G | |
486 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)(21,23)(25,26)(27,28)(30,31)(32,33,35,37,36,39,34,38);(20,21,22,23)(24,25,28,30,29,31,27,26)(33,37)(34,35)(38,39);(24,26,27,31,29,30,28,25)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2719);