Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21776 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#21777 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2308 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C24 | C24×C19 |
| prime radical | C19×#3485 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C24×C19 ◁ G | |
1318 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)(22,30,33,26)(23,27)(24,36,37,28)(25,29)(31,38,45,40)(32,39)(34,47,48,41)(35,42)(43,46)(44,50)(49,51);(20,22)(21,26)(23,31)(24,32)(25,33)(27,40)(28,39)(29,30)(34,44)(35,45)(36,43)(37,46)(38,42)(41,50)(47,49)(48,51);(20,23,25,35)(21,27,29,42)(22,31,33,45)(24,34,37,48)(26,38,30,40)(28,41,36,47)(32,44,46,51)(39,49,43,50);(20,24)(21,28)(22,32)(23,34)(25,37)(26,39)(27,41)(29,36)(30,43)(31,44)(33,46)(35,48)(38,49)(40,50)(42,47)(45,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14765);