Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18316 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#18333 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#392 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
950 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)(23,34)(27,40)(28,38)(29,35)(31,46)(32,33)(36,49)(39,44)(41,47)(42,51)(43,50)(45,48);(20,21,24,29)(22,27,32,42)(23,35,34,26)(25,28,37,43)(30,44,33,41)(31,47,48,39)(36,50,49,38)(40,45,51,46);(23,36)(26,38)(31,46)(34,49)(35,50)(39,51)(40,47)(45,48);(20,22,25,33)(21,27,28,41)(23,31,36,46)(24,32,37,30)(26,39,38,51)(29,42,43,44)(34,48,49,45)(35,47,50,40)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11321);