Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23996 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#23997 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2404 |
| commutator, Frattini, cosocle | C24 | C24×C19 |
| prime radical | C19×#3026 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C24×C19 ◁ G | |
1210 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)(22,26)(23,27)(24,28)(25,29)(30,37)(31,38)(32,39)(33,45)(34,47)(35,41)(36,42)(40,48)(43,51)(44,50)(46,49);(20,22,25,32)(21,26,29,39)(23,33)(24,31,36,44)(27,37)(28,38,42,50)(30,35)(34,46)(40,49)(41,45)(43,48)(47,51);(20,23)(21,27)(22,30)(24,34)(25,35)(26,37)(28,40)(29,41)(31,43)(32,33)(36,48)(38,49)(39,45)(42,47)(44,46)(50,51);(20,24)(21,28)(22,31)(23,34)(25,36)(26,38)(27,40)(29,42)(30,43)(32,44)(33,46)(35,48)(37,49)(39,50)(41,47)(45,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16985);