Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11549 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#13090 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#99 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C22×D4 | C23×C19 |
| prime radical | C23×D4×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C24×C19 ◁ C23×D4×C19 ◁ G | |
910 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25)(26,32,34,39)(27,30,36,38)(28,31)(29,33)(35,37);(24,26,27,35)(25,29,30,32)(28,34,36,33)(31,37,38,39);(21,23)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6078);