Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#19128625 |
| Fitting, socle | C3×C7×C127 ⋊ C2×C3 |
| derived, Hall | C7×C127 ⋊ C2×C32 |
| Hall | C3×#14581887 ⋊ C2 |
| Hall | C7×D127 ⋊ C32 |
| Hall | D127 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C127 ⋊ C2×C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×D127⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #19128625 |
| commutator, cosocle, hypocenter | C7×C127 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C127 | C2×C3 |
| LCS | G ▷ C7×C127 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
471 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#19128625⋊C2, #19128625⋊D3, D3×#19128625, … |
| maximal normal subgroup of | C3×#19128625⋊C2, #19128625⋊D3, D3×#19128625, … |
| maximal quotient of | C3×#24922580, C2×C3×#19128625 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 68);