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×#23834 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | #2398 |
| prime radical | C19×#575 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C8×C19 ◁ G | |
608 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)(22,31,34,44)(23,28)(24,29)(25,39)(26,30)(27,35,41,32)(33,45,48,50)(36,42)(37,43)(38,49)(40,47,51,46);(22,32,34,35)(23,36)(27,31,41,44)(28,42)(33,47,48,46)(37,38)(40,50,51,45)(43,49);(20,22)(21,27)(23,33)(24,32)(25,35)(26,34)(28,40)(29,44)(30,41)(31,39)(36,48)(37,46)(38,47)(42,51)(43,50)(45,49);(20,23,24,37,26,36,25,38)(21,28,29,43,30,42,39,49)(22,33,32,46,34,48,35,47)(27,40,44,50,41,51,31,45)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16822);