Finite Group DatabasebetaFinite Group Databasebeta| order | 7378 |
| isoclinism | isoclinic class of D119 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D119 |
| unambiguous semidirect product | C7⋊(C31×D17) |
| unambiguous semidirect product | C17⋊(D7×C31) |
| Fitting, socle, Hall | C7×C17×C31 ⋊ C2 |
| derived, Hall | C7×C17 ⋊ C2×C31 |
| Hall | C17×C31 ⋊ D7 |
| Hall | C7×C31 ⋊ D17 |
| Sylow | C17 ⋊ D7×C31 |
| Sylow | C7 ⋊ C31×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D119 |
| commutator, hypocenter | C7×C17 | C2×C31 |
| Frattini | C1 | G |
| Fitting, socle | C7×C17×C31 | C2 |
| LCS | G ▷ C7×C17 | |
| UCS | C1 ◁ C31 | |
16 conjugacy classes of subgroups.
1891 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×D119, D7×C31×D17, D119⋊D31, … |
| maximal normal subgroup of | D31×D119, D7×C31×D17, D119⋊D31, … |
| maximal quotient of | C31×Dic119, C2×C31×D119, C3×C31×D119, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7378, 7);