Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#21012 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #386 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#386 |
| prime radical | C19×#3449 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1732 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)(20,21,25,30,26,31,24,29)(22,32,36,43,35,42,34,27)(23,37,38,45,40,28,39,44)(33,46,47,41,49,51,48,50);(20,22)(21,27,31,43)(23,33)(24,34)(25,36)(26,35)(28,41,37,50)(29,42,30,32)(38,47)(39,48)(40,49)(44,51,45,46);(20,23)(21,28)(22,33)(24,38)(25,39)(26,40)(27,41)(29,44)(30,45)(31,37)(32,46)(34,47)(35,49)(36,48)(42,51)(43,50);(20,24,26,25)(21,29,31,30)(22,34,35,36)(23,38,40,39)(27,42,43,32)(28,44,37,45)(33,47,49,48)(41,51,50,46)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14000);