Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#23042 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | D42 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | #2361 |
| prime radical | C19×#3067 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ G | |
824 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)(20,21,27,31)(22,32)(23,37,39,24)(25,30,26,43)(28,42)(29,44,41,38)(33,34)(35,48)(36,47)(40,50)(45,51)(46,49);(20,22,26,35,27,36,25,42)(21,28,43,32,31,48,30,47)(23,33,44,50,39,51,38,46)(24,40,29,45,37,49,41,34);(20,23)(21,29)(22,33)(24,30)(25,38)(26,44)(27,39)(28,45)(31,41)(32,49)(34,48)(35,50)(36,51)(37,43)(40,47)(42,46);(20,24,25,41,27,37,26,29)(21,23,30,38,31,39,43,44)(22,34,35,40,36,45,42,49)(28,46,32,33,48,50,47,51)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16030);