Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×#22547877 |
| derived, Hall | C7×C127 ⋊ C2×C9 |
| Hall | C2×C7×C127 ⋊ C9 |
| Hall | C2×C127 ⋊ C7⋊C9 |
| Sylow | C127 ⋊ C2×C7⋊C9 |
| Hall | C2×C7 ⋊ #11765917 |
| Sylow | C7 ⋊ C2×#11765917 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #14581887 |
| commutator, hypocenter | C7×C127 | C2×C9 |
| Frattini | C3 | C2×#14581887 |
| Fitting, socle, prime radical | C2×C3×C7×C127 | C3 |
| cosocle | C3×C7×C127 | C2×C3 |
| LCS | G ▷ C7×C127 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
1794 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#22547877, #44544639, #44544643, … |
| maximal normal subgroup of | C4×#22547877, #44544639, #44544643, … |
| maximal quotient of | C4×#22547877, C22×#22547877 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 6);