Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33691 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33691 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #3109 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#2190 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C19×#405 ◁ G | |
524 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)(22,30)(23,34)(24,38)(26,39)(28,43)(29,42)(31,36)(32,47)(33,48)(35,49)(37,50)(40,51)(41,46)(44,45);(20,21)(22,26)(23,35)(24,29)(25,27)(28,37)(30,46)(31,45)(32,41)(33,40)(34,49)(36,51)(38,42)(39,47)(43,50)(44,48);(20,22)(21,26)(23,36)(24,31)(25,32)(27,41)(28,44)(29,45)(30,34)(33,38)(35,51)(37,48)(39,43)(40,42)(46,49)(47,50);(21,27)(22,31,32,33)(23,37)(26,40,41,45)(29,42)(30,36,47,48)(34,50)(39,51,46,44)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26679);