Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18132 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18156 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
982 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)(21,27)(23,36)(24,32)(28,44)(29,46)(30,43)(31,38)(33,50)(39,49)(41,42)(45,47)(48,51);(20,21)(22,28)(23,29)(24,38)(25,31)(26,30)(27,32)(33,47)(34,45)(35,42)(36,41)(37,46)(39,51)(40,48)(43,49)(44,50);(20,22,25,34)(21,28,31,45)(23,32,36,24)(26,35,40,37)(27,41,38,29)(30,42,48,46)(33,49,50,39)(43,44,51,47);(20,23,26,33)(21,29,30,47)(22,32,35,49)(24,37,39,34)(25,36,40,50)(27,42,43,28)(31,41,48,44)(38,46,51,45)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11144);