Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #20671 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#20708 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#117 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#381 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C2×C19×#117 ◁ G | |
1260 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)(22,30,32,26)(23,34,36,49)(24,29)(25,28)(27,35,40,50)(31,44)(33,43,47,39)(37,41)(38,46)(42,51)(45,48);(20,22)(21,26)(23,31)(24,33)(25,32)(27,38)(28,30)(29,39)(34,48)(35,46)(36,45)(37,47)(40,42)(41,43)(44,49)(50,51);(20,23)(21,27,28,40)(22,31)(24,35)(25,36)(26,38,30,42)(29,34,41,49)(32,45)(33,46)(37,50)(39,48,43,44)(47,51);(22,32)(26,30)(31,45)(33,47)(38,42)(39,43)(44,48)(46,51)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13696);