Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33359 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33370 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C22×#99 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C2×Q8 | C24×C19 |
| prime radical | C19×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×D4×C19 ◁ C2×C19×2−1+4 ◁ G | |
1208 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)(20,21,24,29,25,30,37,44)(22,27,33,42,31,40,46,50)(23,28,35,43,34,26,36,39)(32,41,47,51,45,38,48,49);(21,26)(23,34)(27,38)(28,30)(29,43)(32,45)(35,36)(39,44)(40,41)(42,51)(47,48)(49,50);(20,22)(21,27)(23,32)(24,33)(25,31)(26,38)(28,41)(29,42)(30,40)(34,45)(35,47)(36,48)(37,46)(39,49)(43,51)(44,50);(22,31)(27,40)(32,45)(33,46)(38,41)(42,50)(47,48)(49,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26358);