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×#11278 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #387 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1442 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
576 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)(22,32,34,47,35,27,41,43)(23,36,39,46,38,28,40,45)(33,42,50,51,49,48,37,44);(20,22)(21,27)(23,37,38,50)(24,34)(25,41)(26,35)(28,44,36,51)(29,32)(30,43)(31,47)(33,39,49,40)(42,45,48,46);(20,23)(21,28,29,36)(22,33)(24,40)(25,39)(26,38)(27,42,32,48)(30,46,31,45)(34,50)(35,49)(37,41)(43,51,47,44)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4266);