Finite Group DatabasebetaFinite Group Databasebeta| order | 18370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D835 |
| unambiguous semidirect product | C5⋊(C11×D167) |
| unambiguous semidirect product | C167⋊(D5×C11) |
| Fitting, socle, Hall | C5×C11×C167 ⋊ C2 |
| derived, Hall | C5×C167 ⋊ C2×C11 |
| Hall | C11×C167 ⋊ D5 |
| Sylow | C167 ⋊ D5×C11 |
| Hall | C5×C11 ⋊ D167 |
| Sylow | C5 ⋊ C11×D167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D835 |
| commutator, cosocle, hypocenter | C5×C167 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C167 | C2 |
| LCS | G ▷ C5×C167 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9185 |
4609 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×C11×D167, D11×D835, D55⋊D167, … |
| maximal normal subgroup of | D5×C11×D167, D11×D835, D55⋊D167, … |
| maximal quotient of | C11×Dic835, C2×C11×D835 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18370, 7);