Finite Group DatabasebetaFinite Group Databasebeta| order | 5430 |
| isoclinism | isoclinic class of D181 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D181 |
| Fitting, socle, Hall | C3×C5×C181 ⋊ C2 |
| derived, Sylow | C181 ⋊ C2×C3×C5 |
| Hall | C5×C181 ⋊ C2×C3 |
| Hall | C3×C181 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D181 |
| commutator, hypocenter | C181 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C181 | C2 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C3×C5 | |
16 conjugacy classes of subgroups.
1380 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×#10624382, C3×#16813740, C3×D5×D181, … |
| maximal normal subgroup of | C3×C5×#10624382, C3×#16813740, C3×D5×D181, … |
| maximal quotient of | C3×C5×Dic181, C2×C3×C5×D181, C5×C9×D181, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5430, 5);