Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18347 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3490 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1072 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)(20,21,24,29)(22,30,31,44)(23,34,37,28)(25,27,38,43)(26,35,41,32)(33,45,47,46)(36,49,51,42)(39,48,40,50);(20,22)(21,26)(23,35)(24,31)(25,33)(27,40)(28,44)(29,41)(30,34)(32,37)(36,50)(38,47)(39,43)(42,46)(45,49)(48,51);(23,36)(28,42)(30,45)(32,48)(34,49)(35,50)(37,51)(44,46);(21,27)(22,31)(26,39)(28,42)(29,43)(30,46)(32,35)(33,47)(34,49)(40,41)(44,45)(48,50)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11335);