Finite Group DatabasebetaFinite Group Databasebeta| order | 19044 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C23⋊Dic23)⋊C9 |
| derived, Sylow | C232 ⋊ C4×C9 |
| Hall | C232⋊C9 ⋊ C4 |
| Hall | C23⋊Dic23 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | (C23⋊D23)⋊C3 |
| commutator, hypocenter | C232 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C232 | C2×C3 |
| LCS | G ▷ C232 | |
| UCS | C1 ◁ C2×C3 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 828 |
Polycyclic presentation:
2,3,23^2,2,3|a^2=e,b^3=f,c^a=c^22,d^a=d^22,c^b=c^7d^17,d^b=c^21d^15564 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19044, 33);