Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23990 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#23992 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#585 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1128 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)(20,21,25,29)(22,26,32,40)(23,27,33,41)(24,35,37,28)(30,43,36,38)(31,45,46,39)(34,48,47,42)(44,50,49,51);(22,30,32,36)(26,38,40,43)(31,44,46,49)(39,50,45,51);(20,22)(21,26)(23,31)(24,36)(25,32)(27,39)(28,43)(29,40)(30,37)(33,46)(34,49)(35,38)(41,45)(42,51)(44,47)(48,50);(20,23)(21,27)(22,31)(24,34)(25,33)(26,39)(28,42)(29,41)(30,44)(32,46)(35,48)(36,49)(37,47)(38,50)(40,45)(43,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16980);