Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#34236 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| prime radical | C2×C19×#532 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
2750 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22)(24,25,28,26)(27,30,31,29)(32,33,36,35)(34,38,39,37);(20,22,23,21)(25,26)(29,30)(33,35)(37,38);(32,34)(33,37)(35,38)(36,39);(24,26,28,25)(27,30,31,29)(32,35,36,33)(34,38,39,37);(24,27,28,31)(25,29,26,30)(32,34)(33,37)(35,38)(36,39)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27224);