Finite Group DatabasebetaFinite Group Databasebeta| order | 19044 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C23 |
| unambiguous semidirect product | (C3⋊D3)⋊(C23⋊D23) |
| Fitting, socle, derived, Hall | C32×C232 ⋊ C22 |
| Sylow | C232 ⋊ D32 |
| Sylow | C32 ⋊ C2×C23⋊D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C232 | C22 |
| LCS | G ▷ C32×C232 | |
| UCS | C1 | |
572 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3174 |
Polycyclic presentation:
2^2,3^2,23^2|d^a=d^2,e^a=e^22,f^a=f^22,c^b=c^2,d^b=d^21593 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19044, 108);