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) = C23×C4 |
| direct product | C19×#20788 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#117 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | #2283 |
| prime radical | C2×#41×C19 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C19×#405 ◁ G | |
608 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)(22,31,34,27)(23,28)(24,29)(25,30)(26,33,40,48)(32,46,35,41)(36,43)(37,44)(38,45)(39,47,42,49)(50,51);(20,22)(21,26,30,40)(23,35)(24,33)(25,34)(27,29,31,45)(28,42,44,39)(32,37)(36,49)(38,48)(41,51,46,43)(47,50);(20,22)(21,27)(23,32)(24,33)(25,34)(26,29)(28,41)(30,31)(35,37)(36,47)(38,48)(39,43)(40,45)(42,51)(44,46)(49,50);(20,23,24,36,25,37,38,50)(21,28,29,43,30,44,45,51)(22,32,33,47,34,35,48,49)(26,39,31,46,40,42,27,41)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13776);