Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D2667 |
| unambiguous semidirect product | C7⋊(C3⋊D381) |
| unambiguous semidirect product | C127⋊(C3⋊D21) |
| Fitting, socle, derived, Hall | C32×C7×C127 ⋊ C2 |
| Hall | C32×C127 ⋊ D7 |
| Hall | C7×C127 ⋊ C3⋊D3 |
| Sylow | C127 ⋊ C3⋊D21 |
| Hall | C32×C7 ⋊ D127 |
| Sylow | C32 ⋊ D889 |
| Sylow | C7 ⋊ C3⋊D381 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C7×C127 | C2 |
| LCS | G ▷ C32×C7×C127 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7,127|b^a=b^2,c^a=c^2,d^a=d^6,e^a=e^1264002 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D2667, D21×D381, C3⋊D21×D127, … |
| maximal normal subgroup of | D3×D2667, D21×D381, C3⋊D21×D127, … |
| maximal quotient of | C3⋊Dic2667, C2×C3⋊D2667 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 92);