Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C127 ⋊ C2×C9 |
| Hall | #22547883 ⋊ C2 |
| Hall | C7×D127 ⋊ C9 |
| Hall | D127 ⋊ C7⋊C9 |
| Sylow | C127 ⋊ C2×C7⋊C9 |
| Sylow | C7 ⋊ #11765919⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C127 | C2×C9 |
| prime radical | C7×D127⋊C3 | C3 |
| cosocle | C7×C127⋊C3 | C2×C3 |
| LCS | G ▷ C7×C127 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7,127|b^3=c,e^a=e^126,d^b=d^2,e^b=e^68,e^c=e^10779 conjugacy classes — view the full character table.
| maximal subgroup of | #30630682⋊C2, C2×#30630688 |
| maximal normal subgroup of | #30630682⋊C2, C2×#30630688 |
| maximal quotient of | #44544712, C2×#30630688 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 45);