Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#7183 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C22⋊C4 |
| commutator | C22 | C4×C16×C19 |
| Frattini, cosocle | C23×C8 | C22×C19 |
| socle | C23×C19 | C22⋊C8 |
| prime radical | C24×C19 | C2×C8 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ C23×C8×C19 ◁ G | |
386 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 2 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25)(26,30,31,28)(27,29)(32,33,34,37,35,38,40,43,36,39,41,44,42,45,46,47);(20,21,22,23)(24,26)(25,28)(27,31)(29,30)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 171);