Finite Group DatabasebetaFinite Group Databasebeta| order | 37380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D35⋊D89 |
| unambiguous semidirect product | D445⋊(C3×D7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D35⋊D89 |
| commutator, cosocle, hypocenter | C5×C7×C89 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C89 | C22 |
| LCS | G ▷ C5×C7×C89 | |
| UCS | C1 ◁ C3 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9345 |
2568 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37380, 70);