Finite Group DatabasebetaFinite Group Databasebeta| order | 1372 |
| isoclinism | isoclinic class of D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D49 |
| Fitting | C2×C7×C49 ⋊ C2 |
| derived | C49 ⋊ C22×C7 |
| Sylow | C7×C49 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D49 |
| commutator, cosocle, hypocenter | C49 | C22×C7 |
| Frattini | C7 | C2×C7×D7 |
| Fitting | C2×C7×C49 | C2 |
| socle | C2×C72 | D7 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C2×C7 | |
42 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, 17);