Finite Group DatabasebetaFinite Group Databasebeta| order | 37380 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C89 · Schur multiplier (H2) = C1 |
| direct product | C3×C89×Dic35 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C89 | D35 |
| commutator, hypocenter | C5×C7 | C3×C4×C89 |
| Frattini | C2 | C3×D35×C89 |
| Fitting, socle, prime radical | C2×C3×C5×C7×C89 | C2 |
| cosocle | C2×C5×C7 | C2×C3×C89 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C2×C3×C89 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 37380 |
10146 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37380, 8);