Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D123⋊D15 |
| Fitting, socle, derived, Hall | C32×C5×C41 ⋊ C22 |
| Hall | C32×C41 ⋊ C2×D5 |
| Hall | C5×C41 ⋊ D32 |
| Hall | C32×C5 ⋊ C2×D41 |
| Sylow | C41 ⋊ D3×D15 |
| Sylow | C32 ⋊ D5×D41 |
| Sylow | C5 ⋊ (C3⋊D3)⋊D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C41 | C22 |
| LCS | G ▷ C32×C5×C41 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,5,41|d^a=d^2,f^a=f^40,c^b=c^2,d^b=d^2,e^b=e^4507 conjugacy classes — view the full character table.
| maximal subgroup of | D123⋊D75, (C3⋊(D41⋊C5))⋊D15, C5×D123⋊D15, … |
| maximal normal subgroup of | (C3⋊(D41⋊C5))⋊D15, C5×D123⋊D15 |
| maximal quotient of | D123⋊D75, C5×D123⋊D15, #49147153, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 122);