Finite Group DatabasebetaFinite Group Databasebeta| order | 5370 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C179 · Schur multiplier (H2) = C1 |
| direct product | D15×C179 |
| unambiguous semidirect product | C3⋊(D5×C179) |
| unambiguous semidirect product | C5⋊(D3×C179) |
| Fitting, socle, Hall | C3×C5×C179 ⋊ C2 |
| derived, Hall | C3×C5 ⋊ C2×C179 |
| Hall | C5×C179 ⋊ D3 |
| Hall | C3×C179 ⋊ D5 |
| Sylow | C5 ⋊ D3×C179 |
| Sylow | C3 ⋊ D5×C179 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C179 | D15 |
| commutator, hypocenter | C3×C5 | C2×C179 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C179 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C179 | |
16 conjugacy classes of subgroups.
1611 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D45×C179, C3⋊D15×C179, C3×D15×C179, … |
| maximal normal subgroup of | C3×D15×C179, C5×D15×C179, C7×D15×C179 |
| maximal quotient of | D45×C179, C3⋊D15×C179, C3×D15×C179, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5370, 7);