Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33359 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33360 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C22×#99 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C2×D4 | C24×C19 |
| prime radical | C19×#3499 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×Q8×C19 ◁ C2×C19×2−1+4 ◁ G | |
1188 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,27)(23,28)(24,29,37,26)(25,30)(31,40)(32,41,47,38)(33,42)(34,43)(35,44,49,39)(36,45)(46,51,48,50);(21,26)(24,37)(27,38)(28,39)(29,30)(32,47)(35,49)(40,50)(41,42)(43,51)(44,45)(46,48);(20,22,25,33)(21,27,30,42)(23,34,36,31)(24,32,37,47)(26,38,29,41)(28,43,45,40)(35,48,49,46)(39,51,44,50);(20,23,25,36)(21,28,30,45)(22,31,33,34)(24,35,37,49)(26,39,29,44)(27,40,42,43)(32,46,47,48)(38,50,41,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26348);