Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12028 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#12930 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#106 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C24×C19 | SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ C23×C8×C19 ◁ G | |
414 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25,27,31,29,34,41,33)(26,35,38,52,39,53,36,50)(28,42,40,32,44,49,54,51)(30,45,47,37,48,43,46,55);(24,26,29,39)(25,30)(27,36,41,38)(28,43,44,45)(31,46)(32,50)(33,47)(34,48)(35,42)(37,54,55,40)(49,53)(51,52);(21,23)(24,27,29,41)(25,31,34,33)(26,36,39,38)(28,40,44,54)(30,46,48,47)(32,49,51,42)(35,50,53,52)(37,45,55,43)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5918);