Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C2×C43 |
| direct product | C19×#14645 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C19 | C24 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C24 | C24×C19 |
| prime radical | C23×D4×C19 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C19 ◁ G | |
1486 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 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)(33,36)(37,39)(40,41,43,44)(42,45,47,46);(25,28)(29,31)(33,36)(34,38)(41,44)(45,46);(24,25)(26,29)(27,28)(30,31)(32,33)(34,37)(35,36)(38,39)(40,41)(42,46)(43,44)(45,47);(24,26,27,30)(25,29,28,31)(32,34,35,38)(33,37,36,39)(40,42)(41,45)(43,47)(44,46)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 7633);