Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11115 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#11116 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #388 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1439 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
848 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)(20,21,25,29,26,30,24,31)(22,32,35,43,36,47,34,27)(23,37,39,45,41,28,40,46)(33,44,38,51,49,48,50,42);(20,22,24,34,26,36,25,35)(21,27,29,32,30,43,31,47)(23,38,39,49,41,50,40,33)(28,44,45,42,37,48,46,51);(20,23)(21,28)(22,33)(24,39)(25,40)(26,41)(27,42)(29,45)(30,37)(31,46)(32,48)(34,38)(35,50)(36,49)(43,51)(44,47)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4104);