Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#20623 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #379 |
| 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 | |
3644 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)(22,31)(23,35,38,28)(24,29)(25,39)(26,30)(27,33)(32,46,48,45)(34,42)(36,50,37,44)(40,43)(41,47,49,51);(20,22)(21,27)(23,32)(24,33)(25,40)(26,34)(28,41)(29,42)(30,43)(31,39)(35,49)(36,47)(37,51)(38,48)(44,46)(45,50);(20,23)(21,28)(22,32)(24,36)(25,37)(26,38)(27,41)(29,44)(30,35)(31,45)(33,47)(34,48)(39,50)(40,51)(42,46)(43,49);(20,24,26,25)(21,29,30,39)(22,33,34,40)(23,36,38,37)(27,42,43,31)(28,44,35,50)(32,47,48,51)(41,46,49,45)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13611);