Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21776 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#21779 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2308 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3485 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1270 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)(20,21,24,29,25,28,37,43)(22,30,33,44,32,26,36,39)(23,27,34,42,35,41,48,51)(31,38,46,49,45,40,47,50);(20,22)(21,26)(23,31)(24,36)(25,32)(27,40)(28,30)(29,44)(33,37)(34,47)(35,45)(38,41)(39,43)(42,49)(46,48)(50,51);(20,23,25,35)(21,27,28,41)(22,31,32,45)(24,34,37,48)(26,38,30,40)(29,42,43,51)(33,46,36,47)(39,49,44,50);(21,28)(24,37)(26,30)(27,41)(33,36)(34,48)(38,40)(46,47)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14767);