Finite Group DatabasebetaFinite Group Databasebeta| order | 19564 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C67⋊#64408 |
| Fitting, socle, derived, Hall | C67×C73 ⋊ C4 |
| Sylow | C73 ⋊ Dic67 |
| Sylow | C67 ⋊ #64408 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C67×C73 | C4 |
| prime radical, cosocle | C67×D73 | C2 |
| LCS | G ▷ C67×C73 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4891 |
Polycyclic presentation:
2^2,67,73|a^2=b,c^a=c^66,d^a=d^27,d^b=d^721276 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19564, 7);