Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#20620 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#120 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#379 |
| prime radical | C2×C19×#585 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
3648 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)(20,21,25,30,26,29,24,37)(22,31,33,27,34,42,38,41)(23,28,35,45,36,43,39,44)(32,47,50,51,49,46,48,40);(20,22)(21,27)(23,32)(24,38)(25,33)(26,34)(28,40)(29,41)(30,42)(31,37)(35,50)(36,49)(39,48)(43,51)(44,46)(45,47);(20,23)(21,28)(22,32)(24,39)(25,35)(26,36)(27,40)(29,43)(30,45)(31,46)(33,50)(34,49)(37,44)(38,48)(41,51)(42,47);(21,29)(27,41)(28,43)(30,37)(31,42)(40,51)(44,45)(46,47)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13608);