Finite Group DatabasebetaFinite Group Databasebeta| order | 1372 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×Dic7 |
| unambiguous semidirect product | C7⋊(C4×C72) |
| derived | C7 ⋊ C4×C72 |
| Sylow | C73 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C72 | D7 |
| commutator, hypocenter | C7 | C4×C72 |
| Frattini | C2 | C72×D7 |
| Fitting, socle, prime radical | C2×C73 | C2 |
| cosocle | C2×C7 | C2×C72 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C72 | |
156 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, 26);