Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11247 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#11310 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #387 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1443 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
532 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)(20,21,25,31,26,29,24,30)(22,32,34,47,35,27,40,42)(23,28,39,46,37,44,38,45)(33,48,36,51,49,41,50,43);(20,22)(21,27)(23,36,37,50)(24,34)(25,40)(26,35)(28,43,44,51)(29,32)(30,42)(31,47)(33,38,49,39)(41,45,48,46);(20,23)(21,28,29,44)(22,33)(24,39)(25,38)(26,37)(27,41,32,48)(30,46,31,45)(34,50)(35,49)(36,40)(42,51,47,43)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4298);