Finite Group DatabasebetaFinite Group Databasebeta| order | 37245 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C191 · Schur multiplier (H2) = C1 |
| direct product | C5×C13⋊C3×C191 |
| unambiguous semidirect product | C13⋊(C3×C5×C191) |
| unambiguous semidirect product | (C5×C13)⋊(C3×C191) |
| unambiguous semidirect product | (C5×C13×C191)⋊C3 |
| Fitting, socle, Hall | C5×C13×C191 ⋊ C3 |
| derived, Sylow | C13 ⋊ C3×C5×C191 |
| Hall | C13×C191 ⋊ C3×C5 |
| Hall | C5×C13 ⋊ C3×C191 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C191 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C3×C5×C191 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C191 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C5×C191 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12415 |
6685 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37245, 3);