Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #365 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#11999 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #106 |
| commutator | C8 | C22×C8×C19 |
| Frattini, cosocle | C4×C8 | C23×C19 |
| socle | C22×C19 | C2×#106 |
| prime radical | C23×C19 | #106 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
234 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
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)(20,21,22,24,23,25,26,27)(28,29)(30,39,42,53)(31,36)(32,45)(33,48)(34,38)(35,41,50,55)(37,46)(40,52,43,57)(44,51)(47,58)(49,54,59,56);(28,30,32,41,33,43,46,56,34,42,47,55,31,40,44,54)(29,35,37,39,36,49,45,52,38,50,51,53,48,59,58,57);(28,31,34,33)(29,36,38,48)(30,40,42,43)(32,44,47,46)(35,49,50,59)(37,45,51,58)(39,52,53,57)(41,54,55,56)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4987);