Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| isoclinism | isoclinic class of C3⋊D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C41 · Schur multiplier (H2) = C3 |
| direct product | C41×C3⋊Dic15 |
| unambiguous semidirect product | C3⋊(C41×Dic15) |
| derived, Hall | C32×C5 ⋊ C4×C41 |
| Hall | C32×C5×C41 ⋊ C4 |
| Hall | C32×C41 ⋊ Dic5 |
| Hall | C5×C41 ⋊ C3⋊Dic3 |
| Sylow | C32 ⋊ Dic5×C41 |
| Sylow | C5 ⋊ C3⋊Dic3×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C41 | C3⋊D15 |
| commutator, hypocenter | C32×C5 | C4×C41 |
| Frattini | C2 | C41×C3⋊D15 |
| Fitting, socle | C2×C32×C5×C41 | C2 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C2×C41 | |
72 conjugacy classes of subgroups.
1968 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×C3⋊Dic75, C3⋊Dic15×C41⋊C5, C41×C3⋊(C3⋊#1039), … |
| maximal normal subgroup of | C3⋊Dic15×C41⋊C5, C5×C41×C3⋊Dic15 |
| maximal quotient of | C41×C3⋊Dic75, C41×C3⋊(C3⋊#1039), C5×C41×C3⋊Dic15, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 65);