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×#21776 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2308 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C24 | C24×C19 |
| prime radical | C19×#3484 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C24×C19 ◁ G | |
1520 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 304 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,28,30,25)(23,31,32,26)(24,27)(29,33)(34,35);(20,22)(21,25)(23,29)(24,30)(26,33)(27,28)(31,34)(32,35);(25,28)(33,34);(20,23)(21,26)(22,29)(24,32)(25,33)(27,31)(28,34)(30,35)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14764);