Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2081 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#11180 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #397 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1440 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
820 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)(22,31,35,27)(23,36,39,46)(24,30)(25,40)(26,29)(28,38,45,41)(32,44)(33,47,34,43)(37,42)(48,50)(49,51);(20,22)(21,27)(23,37)(24,34)(25,33)(26,35)(28,44)(29,31)(30,47)(32,38)(36,48)(39,50)(40,43)(41,49)(42,46)(45,51);(20,23)(21,28,29,45)(22,32)(24,38)(25,41)(26,39)(27,42,31,48)(30,36,40,46)(33,37)(34,50)(35,49)(43,51,47,44)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4168);