Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#24409 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3585 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1336 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)(24,28)(25,29)(27,36)(31,48,49,41)(32,46,39,42)(35,51,50,43)(37,47)(38,45)(40,44);(20,22)(21,26)(23,35)(24,33)(25,39)(27,43)(28,30)(29,46)(31,37)(32,38)(34,51)(36,50)(40,49)(41,44)(42,45)(47,48);(20,23)(21,27)(22,31)(24,36)(25,40)(26,41)(28,34)(29,47)(30,48)(32,50)(33,49)(35,39)(37,38)(42,51)(43,46)(44,45);(20,22)(21,26)(23,31)(24,33)(25,32)(27,41)(28,30)(29,42)(34,48)(35,37)(36,49)(38,39)(40,50)(43,44)(45,46)(47,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17397);