Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11234 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#11246 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #391 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1441 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
624 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)(20,21,25,29,26,30,24,38)(22,31,35,41,34,47,33,27)(23,28,36,45,37,44,39,43)(32,48,49,42,50,46,51,40);(20,22,24,33,26,34,25,35)(21,27,29,31,30,41,38,47)(23,32,36,49,37,50,39,51)(28,42,43,48,44,40,45,46);(20,23,24,36,26,37,25,39)(21,28,29,43,30,44,38,45)(22,32,33,49,34,50,35,51)(27,40,31,46,41,42,47,48)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4234);