Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12503 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C2×C8 |
| direct product | C19×#12516 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C19 | #493 |
| commutator, Frattini, cosocle | C4×C8 | C23×C19 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ C82×C19 ◁ G | |
310 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(22,25)(26,27)(28,29,33,37)(30,38,42,54)(31,43,45,58)(32,46,44,36)(34,47,49,40)(35,50,51,39)(41,57,56,53)(48,55,52,59);(28,30,39,55,32,41,45,47,33,42,50,59,44,56,31,40)(29,34,43,53,36,48,51,54,37,49,58,57,46,52,35,38);(20,21,25,27,23,26,22,24)1330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5504);