Finite Group DatabasebetaFinite Group Databasebeta| order | 18370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C167 · Schur multiplier (H2) = C1 |
| direct product | C2×C11⋊C5×C167 |
| unambiguous semidirect product | (C2×C11)⋊(C5×C167) |
| unambiguous semidirect product | (C2×C11×C167)⋊C5 |
| Fitting, socle, Hall | C2×C11×C167 ⋊ C5 |
| derived, Sylow | C11 ⋊ C2×C5×C167 |
| Hall | C11×C167 ⋊ C2×C5 |
| Hall | C2×C11 ⋊ C5×C167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C167 | C11⋊C5 |
| commutator, cosocle, hypocenter | C11 | C2×C5×C167 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C167 | C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C167 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3674 |
2338 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C11⋊C5×C167, C11⋊C5×Dic167, C167×Dic11⋊C5, … |
| maximal normal subgroup of | C4×C11⋊C5×C167, C11⋊C5×Dic167, C167×Dic11⋊C5, … |
| maximal quotient of | C4×C11⋊C5×C167, C22×C11⋊C5×C167 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18370, 2);