Finite Group DatabasebetaFinite Group Databasebeta| order | 18370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C11⋊C5)⋊D167 |
| unambiguous semidirect product | C167⋊AGL(1,𝔽11) |
| unambiguous semidirect product | D1837⋊C5 |
| Fitting, socle, derived, Hall | C11×C167 ⋊ C2×C5 |
| Hall | C11⋊C5×C167 ⋊ C2 |
| Hall | D1837 ⋊ C5 |
| Sylow | C167 ⋊ AGL(1,𝔽11) |
| Hall | C11⋊C5 ⋊ D167 |
| Sylow | C11 ⋊ C5×D167 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C167 | C2×C5 |
| LCS | G ▷ C11×C167 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1837 |
Polycyclic presentation:
2,5,11,167|c^a=c^10,d^a=d^166,c^b=c^4592 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽11)×D167, C2×(C11⋊C5)⋊D167 |
| maximal normal subgroup of | AGL(1,𝔽11)×D167, C2×(C11⋊C5)⋊D167 |
| maximal quotient of | (C11⋊C5)⋊Dic167, C2×(C11⋊C5)⋊D167 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18370, 12);