Finite Group DatabasebetaFinite Group Databasebeta| order | 16170 |
| isoclinism | isoclinic class of #64418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C5×C11×#64418 |
| Fitting, socle, Hall | C5×C72×C11 ⋊ D3 |
| derived, Hall | #3862 ⋊ C2×C5×C11 |
| Hall | C5×C11×#3862 ⋊ C2 |
| Hall | C11×#3862 ⋊ C2×C5 |
| Hall | C5×#3862 ⋊ C2×C11 |
| Hall | C72×C11 ⋊ C5×D3 |
| Hall | C5×C72 ⋊ D3×C11 |
| Sylow | C72 ⋊ C5×D3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C11 | #64418 |
| commutator, cosocle, hypocenter | #3862 | C2×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C11 | D3 |
| LCS | G ▷ #3862 | |
| UCS | C1 ◁ C5×C11 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 770 |
1100 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D11×#64418, C5×C11×#64418⋊C2, C5×#64418⋊D11, … |
| maximal normal subgroup of | C5×D11×#64418, C5×C11×#64418⋊C2, C5×#64418⋊D11, … |
| maximal quotient of | C5×C11×#10596868, C2×C5×C11×#64418 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16170, 88);