Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18284 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18298 |
| 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 ◁ C23×C4×C19 ◁ G | |
1024 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)(21,28)(22,33)(23,38)(24,34)(29,47)(30,49)(31,40)(32,46)(35,39)(36,37)(41,42)(43,51)(44,45)(48,50);(20,21)(22,29)(23,30)(24,40)(25,43)(26,31)(27,32)(28,34)(33,49)(35,50)(36,45)(37,48)(38,44)(39,47)(41,46)(42,51);(20,22,27,37)(21,29,32,48)(23,34,38,41)(24,39,42,35)(25,33,26,36)(28,44,46,30)(31,45,43,49)(40,47,51,50);(20,23,26,35)(21,30,31,50)(22,34,36,24)(25,39,27,38)(28,45,40,29)(32,44,43,47)(33,42,37,41)(46,49,51,48)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11286);