Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23882 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23885 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1662 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)(22,33)(23,38)(24,41)(25,31)(26,30)(27,32)(28,36)(29,40)(34,43)(35,44)(37,47)(39,46)(42,45)(48,50)(49,51);(20,22)(21,28)(23,34)(24,35)(25,42)(26,36)(27,37)(29,44)(30,47)(31,33)(32,45)(38,48)(39,51)(40,50)(41,49)(43,46);(20,23,27,24)(21,29,32,46)(22,34,37,35)(25,40,26,39)(28,43,45,44)(30,38,31,41)(33,48,47,49)(36,51,42,50);(20,24,27,23)(21,29,32,46)(22,35,37,34)(25,39,26,40)(28,44,45,43)(30,38,31,41)(33,49,47,48)(36,50,42,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16873);