Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #22284 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#22286 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2328 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3155 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
820 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,25)(23,34,38,32)(24,39)(26,30)(27,31)(28,37,44,36)(29,40)(33,42)(35,48,51,43)(41,45)(46,49,47,50);(20,22,26,31,27,30,25,21)(23,28,36,34,38,44,37,32)(24,33,41,45,42,39,40,29)(35,43,49,47,51,48,50,46);(20,23)(21,28,31,44)(22,32,30,34)(24,35)(25,36)(26,37)(27,38)(29,43,45,48)(33,46,39,47)(40,49)(41,50)(42,51);(20,24,26,41,27,42,25,40)(21,29,22,33,31,45,30,39)(23,35,37,50,38,51,36,49)(28,43,32,46,44,48,34,47)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15274);