Finite Group DatabasebetaFinite Group Databasebeta| order | 18205 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C11×C331 ⋊ C5 |
| Sylow | C331 ⋊ C11⋊C5 |
| Sylow | C11 ⋊ C331⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C331 | C5 |
| LCS | G ▷ C11×C331 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3641 |
Polycyclic presentation:
5,11,331|b^a=b^3,c^a=c^64733 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#32911658, #49138685, #49138691, … |
| maximal normal subgroup of | C2×#32911658, #49138685, #49138691, … |
| maximal quotient of | C2×#32911658 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18205, 5);