Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21782 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#21784 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2308 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1278 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)(22,30,33,26)(23,34,36,46)(24,29)(25,28)(27,35,43,38)(31,47)(32,45,37,41)(39,44)(40,48)(42,50)(49,51);(20,22)(21,26)(23,31)(24,37)(25,33)(27,42)(28,30)(29,45)(32,39)(34,51)(35,50)(36,49)(38,48)(40,43)(41,44)(46,47);(20,23,25,36)(21,27,28,43)(22,31,33,49)(24,38,39,35)(26,40,30,42)(29,46,44,34)(32,50,37,48)(41,47,45,51);(20,22)(21,26)(23,31)(24,32)(25,33)(27,40)(28,30)(29,41)(34,51)(35,48)(36,49)(37,39)(38,50)(42,43)(44,45)(46,47)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14772);