Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#24474 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3586 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1298 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)(20,21,25,30,26,24,43,29)(22,31,35,33,36,45,34,27)(23,37,41,39,42,47,40,28)(32,44,49,51,50,48,38,46);(20,22)(21,27)(23,38)(24,33)(25,35)(26,36)(28,46)(29,45)(30,31)(32,41)(34,43)(37,44)(39,51)(40,50)(42,49)(47,48);(20,23,26,42)(21,28,24,39)(22,32,36,50)(25,40,43,41)(27,44,33,48)(29,37,30,47)(31,46,45,51)(34,49,35,38);(20,24)(21,26)(22,33)(23,39)(25,29)(27,36)(28,42)(30,43)(31,34)(32,48)(35,45)(37,40)(38,51)(41,47)(44,50)(46,49)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17462);