Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#11268 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C19 | C2×D4 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C19 ◁ C22×C42×C19 ◁ G | |
798 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 4864 |
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)(24,25,26,27)(28,29,31,30)(33,38)(34,39)(35,36);(20,21)(22,23)(28,30,31,29)(32,33,35,38,37,39,36,34);(21,23)(29,30)(32,34,35,33,37,38,36,39)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4256);