Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#11094 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #392 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1439 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
868 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)(20,21,25,29,26,30,24,39)(22,27,34,42,33,43,32,48)(23,35,38,28,37,45,40,44)(31,46,47,41,36,50,49,51);(20,22)(21,27)(23,36,37,31)(24,32)(25,34)(26,33)(28,41,44,51)(29,42)(30,43)(35,46,45,50)(38,49,40,47)(39,48);(20,23)(21,28)(22,31)(24,40)(25,38)(26,37)(27,41)(29,45)(30,44)(32,49)(33,36)(34,47)(35,39)(42,50)(43,51)(46,48)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4082);