Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23434 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#127 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#392 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1916 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 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)(23,36)(24,41)(25,30)(26,29)(27,33)(28,39)(32,49)(34,43)(35,44)(37,48)(38,46)(40,47)(42,50)(45,51);(20,22)(21,27)(23,37)(24,34)(25,33)(26,35)(28,45)(29,43)(30,44)(31,41)(32,38)(36,42)(39,50)(40,51)(46,48)(47,49);(20,23)(21,28)(22,32)(24,38)(25,39)(26,40)(27,42)(29,46)(30,47)(31,48)(33,37)(34,51)(35,50)(36,41)(43,49)(44,45);(21,29)(27,43)(28,46)(30,41)(31,44)(36,47)(42,49)(45,48)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16422);