Finite Group DatabasebetaFinite Group Databasebeta| order | 11190 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D373⋊C3 |
| unambiguous semidirect product | D373⋊(C3×C5) |
| unambiguous semidirect product | (C373⋊C3)⋊(C2×C5) |
| unambiguous semidirect product | (C5×D373)⋊C3 |
| Fitting, socle, Hall | C5×C373 ⋊ C2×C3 |
| derived, Sylow | C373 ⋊ C2×C3×C5 |
| Hall | C5×C373⋊C3 ⋊ C2 |
| Hall | C5×D373 ⋊ C3 |
| Hall | C373⋊C3 ⋊ C2×C5 |
| Hall | D373 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D373⋊C3 |
| commutator, cosocle, hypocenter | C373 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C373 | C2×C3 |
| LCS | G ▷ C373 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
340 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#13093637⋊C3, #21418654⋊C3, D5×D373⋊C3, … |
| maximal normal subgroup of | C5×#13093637⋊C3, #21418654⋊C3, D5×D373⋊C3, … |
| maximal quotient of | C5×Dic373⋊C3, C2×C5×D373⋊C3, C5×D373⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11190, 10);