Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#11000 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #390 |
| 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)(22,30)(23,34,36,27)(24,37)(25,29)(26,32)(28,39)(31,45,47,51)(33,44)(35,43,50,48)(38,41)(40,49,42,46);(20,22)(21,26)(23,31)(24,38)(25,33)(27,42)(28,44)(29,41)(30,37)(32,39)(34,40)(35,49)(36,47)(43,45)(46,50)(48,51);(20,23)(21,27)(22,31)(24,35)(25,36)(26,40)(28,43)(29,34)(30,45)(32,46)(33,47)(37,48)(38,49)(39,50)(41,42)(44,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3988);