Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#18386 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#1595 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
984 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)(21,26)(22,30)(23,35)(27,41)(28,39)(29,36)(31,45)(32,48)(33,34)(37,50)(40,47)(42,46)(43,51)(44,49);(20,21)(22,31)(23,36)(24,29)(25,28)(26,35)(27,33)(30,42)(32,40)(34,47)(37,51)(38,43)(39,50)(41,44)(45,48)(46,49);(23,37)(26,39)(32,48)(35,50)(36,51)(40,45)(41,46)(44,49);(20,22,25,34)(21,27,28,42)(23,32,37,48)(24,33,38,30)(26,40,39,45)(29,31,43,47)(35,49,50,44)(36,46,51,41)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11374);