Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#11273 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #394 |
| 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)(22,26,31,41)(23,33)(24,37)(25,28)(27,35)(29,38)(30,44,34,49)(32,48,47,40)(36,50)(39,51,42,46)(43,45);(20,22,24,32,25,31,38,47)(21,26,29,40,28,41,37,48)(23,34,35,51,36,30,45,46)(27,42,33,49,43,39,50,44);(20,23)(21,27,28,43)(22,30,31,34)(24,35)(25,36)(26,39)(29,33,37,50)(32,46,47,51)(38,45)(40,44)(41,42)(48,49)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4261);