Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#11037 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #392 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1438 |
| prime radical | C2×C19×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1252 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)(22,31,33,27,34,43,40,42)(23,28,37,45,38,47,36,46)(32,44,49,51,50,48,35,41);(20,22)(21,27)(23,35)(24,40)(25,33)(26,34)(28,44)(29,43)(30,42)(31,39)(32,37)(36,50)(38,49)(41,46)(45,51)(47,48);(20,23)(21,28)(22,32)(24,36)(25,37)(26,38)(27,41)(29,45)(30,47)(31,48)(33,49)(34,50)(35,40)(39,46)(42,51)(43,44)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4025);