Finite Group DatabasebetaFinite Group Databasebeta| order | 18205 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C5×C331⋊C11 |
| unambiguous semidirect product | (C5×C331)⋊C11 |
| Fitting, socle, Hall | C5×C331 ⋊ C11 |
| derived, Sylow | C331 ⋊ C5×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C331⋊C11 |
| commutator, cosocle, hypocenter | C331 | C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C331 | C11 |
| LCS | G ▷ C331 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1655 |
205 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C5×C331⋊C11, C5×D331⋊C11, D5×C331⋊C11, … |
| maximal normal subgroup of | C2×C5×C331⋊C11, C5×D331⋊C11, D5×C331⋊C11, … |
| maximal quotient of | C2×C5×C331⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18205, 2);