Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#11003 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #392 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1438 |
| prime radical | C19×#3449 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1292 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 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)(22,31)(23,35,38,46)(24,39)(25,29)(26,30)(27,33)(28,37,45,36)(32,44,49,41)(34,42)(40,43)(47,48,51,50);(20,22)(21,27)(23,32)(24,40)(25,33)(26,34)(28,44)(29,42)(30,43)(31,39)(35,51)(36,50)(37,48)(38,49)(41,45)(46,47);(20,23)(21,28)(22,32)(24,37)(25,36)(26,38)(27,41)(29,46)(30,45)(31,47)(33,50)(34,49)(35,39)(40,48)(42,51)(43,44)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3991);