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×#11234 |
| 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 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
640 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)(22,31)(23,35,38,50)(24,39)(25,29)(26,30)(27,33)(28,37,45,36)(32,41,48,44)(34,42)(40,43)(46,47,49,51);(20,22,24,33,26,34,25,40)(21,27,29,31,30,43,39,42)(23,32,36,47,38,48,37,51)(28,44,35,49,45,41,50,46);(20,23,24,36,26,38,25,37)(21,28,29,35,30,45,39,50)(22,32,33,47,34,48,40,51)(27,41,31,46,43,44,42,49)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4222);