Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11115 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#11313 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #388 |
| 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)(22,31,34,27)(23,35)(24,39)(25,30)(26,29)(28,37)(32,49,51,45)(33,43,40,44)(36,42,50,48)(38,47)(41,46);(20,22,24,33,26,34,25,40)(21,27,39,44,29,31,30,43)(23,36,37,32,38,50,41,51)(28,45,47,42,46,49,35,48);(20,23)(21,28,29,46)(22,32)(24,37)(25,41)(26,38)(27,42,31,48)(30,35,39,47)(33,50)(34,51)(36,40)(43,45,44,49)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4301);