Finite Group DatabasebetaFinite Group Databasebeta| order | 4446 |
| automorphism | Aut(G) order 2881008 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2223 |
| unambiguous semidirect product | C9⋊D247 |
| unambiguous semidirect product | C13⋊D171 |
| unambiguous semidirect product | C19⋊D117 |
| Fitting, derived, Hall | C9×C13×C19 ⋊ C2 |
| Hall | C13×C19 ⋊ D9 |
| Hall | C9×C19 ⋊ D13 |
| Hall | C9×C13 ⋊ D19 |
| Sylow | C19 ⋊ D117 |
| Sylow | C13 ⋊ D171 |
| Sylow | C9 ⋊ D247 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C13×C19 | C2 |
| Frattini | C3 | D741 |
| socle | C3×C13×C19 | D3 |
| LCS | G ▷ C9×C13×C19 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2223 |
Polycyclic presentation:
2,3,13,19,3|b^3=e^2,b^a=b^2e,c^a=c^12,d^a=d^18,e^a=e^21113 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D2223, D11115, C7×D2223, … |
| maximal normal subgroup of | C5×D2223, C7×D2223 |
| maximal quotient of | C5×D2223, D11115, C7×D2223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4446, 24);