Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #365 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#12563 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #106 |
| commutator | C8 | C2×C42×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C22×C19 | C2×#106 |
| prime radical | C24×C19 | SD16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ C23×C8×C19 ◁ G | |
570 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)(26,37,40,50)(27,33)(28,45)(29,46)(30,47)(31,36)(32,39,49,41)(34,44)(35,43)(38,51,42,55)(48,53,52,54);(21,23)(24,26,29,41,30,42,43,53,31,40,28,39,27,38,44,54)(25,32,35,50,33,48,46,55,36,49,34,37,47,52,45,51);(24,27,31,30)(25,33,36,47)(26,38,40,42)(28,43,29,44)(32,48,49,52)(34,45,35,46)(37,51,50,55)(39,53,41,54)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5551);