Finite Group DatabasebetaFinite Group Databasebeta| order | 11580 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic193⋊C3 |
| unambiguous semidirect product | Dic193⋊(C3×C5) |
| unambiguous semidirect product | (C5×Dic193)⋊C3 |
| derived, Sylow | C193 ⋊ C3×C4×C5 |
| Hall | C5×Dic193 ⋊ C3 |
| Hall | C5×C193⋊C3 ⋊ C4 |
| Hall | C5×C193 ⋊ C3×C4 |
| Hall | Dic193 ⋊ C3×C5 |
| Hall | C193⋊C3 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D193⋊C3 |
| commutator, hypocenter | C193 | C3×C4×C5 |
| Frattini | C2 | C5×D193⋊C3 |
| Fitting, socle | C2×C5×C193 | C2×C3 |
| prime radical | C2×C5×C193⋊C3 | C2 |
| cosocle | C2×C193 | C2×C3×C5 |
| LCS | G ▷ C193 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
380 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×Dic193⋊C3, C5×C3⋊(Dic193⋊C3) |
| maximal normal subgroup of | C3×C5×Dic193⋊C3 |
| maximal quotient of | C5×Dic193⋊C9, C3×C5×Dic193⋊C3, C5×C3⋊(Dic193⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11580, 10);