Finite Group DatabasebetaFinite Group Databasebeta| order | 15372 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D549 |
| unambiguous semidirect product | (C2×C9)⋊(C7×D61) |
| unambiguous semidirect product | (C2×C61)⋊(C7×D9) |
| Fitting | C2×C7×C9×C61 ⋊ C2 |
| derived, Hall | C9×C61 ⋊ C22×C7 |
| Hall | C7×C9×C61 ⋊ C22 |
| Hall | C7×C61 ⋊ C2×D9 |
| Hall | C7×C9 ⋊ C2×D61 |
| Sylow | C61 ⋊ C2×C7×D9 |
| Sylow | C9 ⋊ C2×C7×D61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D549 |
| commutator, cosocle, hypocenter | C9×C61 | C22×C7 |
| Frattini | C3 | C2×C7×D183 |
| Fitting | C2×C7×C9×C61 | C2 |
| socle | C2×C3×C7×C61 | D3 |
| LCS | G ▷ C9×C61 | |
| UCS | C1 ◁ C2×C7 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7686 |
3864 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15372, 74);