Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊D615 |
| unambiguous semidirect product | (C2×C3)⋊D615 |
| unambiguous semidirect product | (C2×C5)⋊(C3⋊D123) |
| unambiguous semidirect product | (C2×C41)⋊(C3⋊D15) |
| Fitting, socle | C2×C32×C5×C41 ⋊ C2 |
| derived, Hall | C32×C5×C41 ⋊ C22 |
| Hall | C32×C41 ⋊ C2×D5 |
| Hall | C5×C41 ⋊ C2×C3⋊D3 |
| Hall | C32×C5 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×C3⋊D15 |
| Sylow | C32 ⋊ C2×D205 |
| Sylow | C5 ⋊ C2×C3⋊D123 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D615 |
| commutator, hypocenter | C32×C5×C41 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C5×C41 | C2 |
| LCS | G ▷ C32×C5×C41 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
1848 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3⋊D3075, C2×C3⋊(C3⋊(C5⋊(D41⋊C5))), D5×C3⋊D615, … |
| maximal normal subgroup of | C2×C3⋊(C3⋊(C5⋊(D41⋊C5))), C2×C5×C3⋊D615 |
| maximal quotient of | C2×C3⋊D3075, D5×C3⋊D615, C2×C5×C3⋊D615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 138);