Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2081 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#11307 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #397 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1443 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
548 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)(22,26,31,40)(23,33)(24,37)(25,28)(27,35)(29,38)(30,39,44,51)(32,46,45,41)(34,47,49,42)(36,43)(48,50);(20,22)(21,26,28,40)(23,34,35,49)(24,32)(25,31)(27,42)(29,41,37,46)(30,36,44,50)(33,47)(38,45)(39,48)(43,51);(20,23)(21,27,28,33)(22,30,31,44)(24,36)(25,35)(26,39)(29,43,37,48)(32,34,45,49)(38,50)(40,51)(41,42)(46,47)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4295);