Finite Group DatabasebetaFinite Group Databasebeta| order | 18370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C167 · Schur multiplier (H2) = C1 |
| direct product | D55×C167 |
| unambiguous semidirect product | C5⋊(D11×C167) |
| unambiguous semidirect product | C11⋊(D5×C167) |
| Fitting, socle, Hall | C5×C11×C167 ⋊ C2 |
| derived, Hall | C5×C11 ⋊ C2×C167 |
| Hall | C11×C167 ⋊ D5 |
| Hall | C5×C167 ⋊ D11 |
| Sylow | C11 ⋊ D5×C167 |
| Sylow | C5 ⋊ D11×C167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C167 | D55 |
| commutator, cosocle, hypocenter | C5×C11 | C2×C167 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C167 | C2 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C167 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9185 |
4843 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D55×D167, D5×D11×C167, D55⋊D167, … |
| maximal normal subgroup of | D55×D167, D5×D11×C167, D55⋊D167, … |
| maximal quotient of | C167×Dic55, C2×D55×C167 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18370, 8);