Finite Group DatabasebetaFinite Group Databasebeta| order | 1372 |
| isoclinism | isoclinic class of D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic49 |
| derived | C49 ⋊ C4×C7 |
| Sylow | C7×C49 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D49 |
| commutator, hypocenter | C49 | C4×C7 |
| Frattini | C2×C7 | C7×D7 |
| Fitting | C2×C7×C49 | C2 |
| socle, prime radical | C2×C72 | D7 |
| cosocle | C2×C49 | C2×C7 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C2×C7 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 196 |
364 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1372, 5);