Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3019 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#20939 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#120 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#386 |
| prime radical | C2×C19×#575 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1668 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)(22,31,34,43)(23,35)(24,30)(25,39)(26,29)(27,33,42,38)(28,36)(32,47,50,41)(37,45)(40,44)(46,48,51,49);(20,22,24,38,26,34,25,33)(21,27,30,43,29,42,39,31)(23,32,36,49,37,50,40,48)(28,41,45,51,44,47,35,46);(20,23)(21,28)(22,32)(24,36)(25,40)(26,37)(27,41)(29,44)(30,45)(31,46)(33,48)(34,50)(35,39)(38,49)(42,47)(43,51);(21,29)(27,42)(28,44)(30,39)(31,43)(35,45)(41,47)(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, 13927);