Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3068 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#21000 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#121 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#386 |
| prime radical | C2×C19×#575 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1704 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)(22,26,31,40)(23,33,34,45)(24,29)(25,28)(27,35,42,37)(30,46)(32,41,36,44)(38,43)(39,49)(47,50)(48,51);(20,22)(21,26,28,40)(23,30)(24,36)(25,31)(27,39,42,51)(29,44,43,41)(32,38)(33,50,45,46)(34,47)(35,49)(37,48);(20,23)(21,27)(22,30)(24,37)(25,34)(26,39)(28,42)(29,45)(31,47)(32,49)(33,43)(35,38)(36,48)(40,51)(41,50)(44,46);(22,31)(26,40)(30,47)(32,36)(39,51)(41,44)(46,50)(48,49)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13988);