Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#23753 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#400 |
| prime radical | C24×C19 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
648 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)(20,21,24,29,25,30,26,41)(22,31,33,43,35,46,34,27)(23,36,39,50,38,28,40,45)(32,44,48,51,47,49,37,42);(20,22,26,33,25,35,24,34)(21,27,41,31,30,43,29,46)(23,37,40,32,38,48,39,47)(28,44,50,51,36,49,45,42);(20,23,24,39,25,38,26,40)(21,28,29,45,30,36,41,50)(22,32,33,48,35,47,34,37)(27,42,31,44,43,51,46,49);(23,38)(28,36)(32,47)(37,48)(39,40)(42,51)(44,49)(45,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16741);