Finite Group DatabasebetaFinite Group Databasebeta| order | 1372 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C49 · Schur multiplier (H2) = C2 |
| direct product | C2×D7×C49 |
| unambiguous semidirect product | C7⋊(C22×C49) |
| unambiguous semidirect product | (C2×C7)⋊(C2×C49) |
| Fitting | C2×C7×C49 ⋊ C2 |
| derived | C7 ⋊ C22×C49 |
| Sylow | C7×C49 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C49 | D7 |
| commutator, hypocenter | C7 | C22×C49 |
| Frattini | C7 | C2×C7×D7 |
| Fitting | C2×C7×C49 | C2 |
| socle | C2×C72 | C2×C7 |
| prime radical | C2×C7×D7 | C7 |
| cosocle | C72 | C22×C7 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C49 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 196 |
490 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1372, 18);