Finite Group DatabasebetaFinite Group Databasebeta| order | 38612 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C7×Dic197⋊C7 |
| unambiguous semidirect product | Dic197⋊C72 |
| unambiguous semidirect product | (C7×Dic197)⋊C7 |
| derived, Sylow | C197 ⋊ C4×C72 |
| Hall | C7×C197⋊C7 ⋊ C4 |
| Hall | Dic197 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D197⋊C7 |
| commutator, hypocenter | C197 | C4×C72 |
| Frattini | C2 | C7×D197⋊C7 |
| Fitting, socle | C2×C7×C197 | C2×C7 |
| prime radical | C2×C7×C197⋊C7 | C2 |
| cosocle | C2×C197 | C2×C72 |
| LCS | G ▷ C197 | |
| UCS | C1 ◁ C2×C7 | |
60 conjugacy classes of subgroups.
392 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38612, 20);