Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23360 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#23360 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2380 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
688 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 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)(22,30,33,26)(23,34,37,48)(24,28)(25,29)(27,36,44,50)(31,42)(32,45,38,41)(35,40)(39,43)(46,49)(47,51);(20,22)(21,26)(23,35)(24,38)(25,33)(27,42)(28,45)(29,30)(31,36)(32,39)(34,46)(37,49)(40,48)(41,43)(44,51)(47,50);(20,23,24,36,25,37,39,50)(21,27,43,48,29,44,28,34)(22,31,32,35,33,47,38,49)(26,40,45,42,30,46,41,51);(21,28,29,43)(26,41,30,45)(27,34,44,48)(40,51,46,42)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16348);