Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C2×C42 |
| direct product | C19×#14464 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C19 | C24 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C24 | C24×C19 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C19 ◁ G | |
1146 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 4864 |
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)(25,28)(26,30)(32,33,35,36)(34,37,38,39)(41,42)(45,46);(33,36)(34,38)(40,41,44,42)(43,46,47,45);(24,25)(26,29)(27,28)(30,31)(32,33)(34,37)(35,36)(38,39)(40,42,44,41)(43,46,47,45);(24,26,27,30)(25,29,28,31)(32,34)(33,37)(35,38)(36,39)(40,43)(41,45)(42,46)(44,47)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 7452);