Finite Group DatabasebetaFinite Group Databasebeta| order | 37926 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C43 · Schur multiplier (H2) = C1 |
| direct product | C7×C43×D63 |
| unambiguous semidirect product | C7⋊(C7×D9×C43) |
| unambiguous semidirect product | C9⋊(C7×D7×C43) |
| Fitting, Hall | C72×C9×C43 ⋊ C2 |
| derived | C7×C9 ⋊ C2×C7×C43 |
| Hall | C72×C43 ⋊ D9 |
| Hall | C72×C9 ⋊ C2×C43 |
| Hall | C9×C43 ⋊ C7×D7 |
| Sylow | C72 ⋊ D9×C43 |
| Sylow | C9 ⋊ C7×D7×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C43 | D63 |
| commutator, cosocle, hypocenter | C7×C9 | C2×C7×C43 |
| Frattini | C3 | C7×D21×C43 |
| Fitting | C72×C9×C43 | C2 |
| socle | C3×C72×C43 | D3 |
| LCS | G ▷ C7×C9 | |
| UCS | C1 ◁ C7×C43 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5418 |
9933 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37926, 181);