Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13027 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #459 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1879 |
| prime radical | C19×#3414 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ C2×C4×C8×C19 ◁ G | |
484 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)(20,21,25,30,26,32,43,50,27,33,23,40,42,45,24,31)(22,34,37,47,38,46,36,48,39,51,35,29,44,49,41,28);(20,22)(21,28,33,48)(23,41)(24,35)(25,36)(26,44)(27,39)(29,45,47,32)(30,46,40,49)(31,51,50,34)(37,43)(38,42);(20,22)(21,29)(23,41)(24,35)(25,36)(26,44)(27,39)(28,45)(30,34)(31,46)(32,48)(33,47)(37,43)(38,42)(40,51)(49,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6015);