Finite Group DatabasebetaFinite Group Databasebeta| order | 1372 |
| isoclinism | isoclinic class of C7⋊D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊Dic49 |
| unambiguous semidirect product | C49⋊Dic7 |
| derived, Sylow | C7×C49 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C7⋊D49 |
| commutator, hypocenter | C7×C49 | C4 |
| Frattini | C2×C7 | C7⋊D7 |
| Fitting, cosocle | C2×C7×C49 | C2 |
| socle, prime radical | C2×C72 | D7 |
| LCS | G ▷ C7×C49 | |
| UCS | C1 ◁ C2 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1372 |
Polycyclic presentation:
2^2,7^3|a^2=b,d^7=e,c^a=c^6,d^a=d^6e^6,e^a=e^6346 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1372, 9);