Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#23609 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C23×C19 | C22×D4 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ C22×C42×C19 ◁ G | |
1138 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(28,29)(30,39)(31,40)(32,36)(33,37)(34,38)(35,42)(41,43);(24,25)(26,27)(28,30,32,40,34,35,33,41)(29,31,37,39,38,43,36,42);(21,23)(25,27)(28,31)(29,35)(30,38)(32,42)(33,39)(34,43)(36,41)(37,40);(28,32,34,33)(29,36,38,37)(30,40,35,41)(31,42,43,39)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16597);