Finite Group DatabasebetaFinite Group Databasebeta| order | 37510 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C112 · Schur multiplier (H2) = C11 |
| direct product | C112×D155 |
| unambiguous semidirect product | C5⋊(C112×D31) |
| unambiguous semidirect product | C31⋊(D5×C112) |
| Fitting, socle, Hall | C5×C112×C31 ⋊ C2 |
| derived, Hall | C5×C31 ⋊ C2×C112 |
| Hall | C112×C31 ⋊ D5 |
| Hall | C5×C112 ⋊ D31 |
| Sylow | C31 ⋊ D5×C112 |
| Sylow | C5 ⋊ C112×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C112 | D155 |
| commutator, cosocle, hypocenter | C5×C31 | C2×C112 |
| Frattini | C1 | G |
| Fitting, socle | C5×C112×C31 | C2 |
| LCS | G ▷ C5×C31 | |
| UCS | C1 ◁ C112 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18755 |
9559 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37510, 180);