Finite Group DatabasebetaFinite Group Databasebeta| order | 1372 |
| isoclinism | isoclinic class of C7⋊(C7⋊D7) |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C73 |
| unambiguous semidirect product | C7⋊(C7⋊Dic7) |
| derived, Sylow | C73 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊(C7⋊D7) |
| commutator, hypocenter | C73 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C73 | C2 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2 | |
348 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1372 |
Polycyclic presentation:
2^2,7^3|a^2=b,c^a=c^6,d^a=d^6,e^a=e^6346 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1372, 28);