Finite Group DatabasebetaFinite Group Databasebeta| order | 15666 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C373 ⋊ C2×C3 |
| Hall | #21463179 ⋊ C2 |
| Hall | C7×D373 ⋊ C3 |
| Hall | D373 ⋊ ΓL(1,𝔽8) |
| Sylow | C373 ⋊ C2×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ D373⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C373 | C2×C3 |
| LCS | G ▷ C7×C373 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2611 |
Polycyclic presentation:
2,3,7,373|d^a=d^372,c^b=c^2,d^b=d^88444 conjugacy classes — view the full character table.
| maximal subgroup of | #44531267, #30627835⋊C2, #44531273, … |
| maximal normal subgroup of | #44531267, #30627835⋊C2, #44531273, … |
| maximal quotient of | #44531255, C2×#30627835 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15666, 16);