Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11234 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#11245 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #391 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1441 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
624 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 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)(22,30)(23,27,35,42)(24,36)(25,29)(26,32)(28,37)(31,45,47,43)(33,44)(34,49,50,41)(38,46,40,51)(39,48);(20,22,24,32,25,33,37,48)(21,26,28,30,29,39,36,44)(23,31,34,46,35,47,50,51)(27,40,41,45,42,38,49,43);(20,23,24,34,25,35,37,50)(21,27,28,41,29,42,36,49)(22,31,32,46,33,47,48,51)(26,38,30,43,39,40,44,45)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4233);