Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#22950 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | C2×C4×D4 |
| prime radical | C19×#525 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C19×C22⋊C8 ◁ G | |
768 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(25,27)(28,29,32,36,33,31,40,35)(30,34,39,42,38,37,43,41);(20,21)(22,25)(23,24)(26,27)(28,30,32,39,33,38,40,43)(29,34,36,42,31,37,35,41);(20,22,23,26)(21,25,24,27)(28,31)(29,33)(30,37)(32,35)(34,38)(36,40)(39,41)(42,43);(21,24)(25,27)(30,38)(34,37)(39,43)(41,42)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15938);