Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33571 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C24×C19 |
| prime radical | C19×#3018 | C2 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C2×#41×C19 ◁ G | |
1084 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)(22,32)(23,29)(24,38)(25,28)(26,31)(27,34)(30,41)(33,44)(35,48)(36,47)(37,45)(39,46)(40,49)(42,51)(43,50);(20,22,26,36)(21,27,31,44)(23,34,24,33)(25,40,41,35)(28,42,30,43)(29,47,38,32)(37,50,39,51)(45,49,46,48);(21,28)(25,41)(27,42)(29,45)(30,31)(32,48)(35,40)(37,39)(38,46)(43,44)(47,49)(50,51);(20,23,26,24)(21,29,31,38)(22,33,36,34)(25,37,41,39)(27,32,44,47)(28,45,30,46)(35,50,40,51)(42,48,43,49)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26559);