Finite Group DatabasebetaFinite Group Databasebeta| order | 15855 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×C151⋊C5 |
| unambiguous semidirect product | (C3×C151)⋊(C5×C7) |
| unambiguous semidirect product | (C3×C7×C151)⋊C5 |
| Fitting, socle, Hall | C3×C7×C151 ⋊ C5 |
| derived, Sylow | C151 ⋊ C3×C5×C7 |
| Hall | C7×C151 ⋊ C3×C5 |
| Hall | C3×C151 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | C151⋊C5 |
| commutator, cosocle, hypocenter | C151 | C3×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C151 | C5 |
| LCS | G ▷ C151 | |
| UCS | C1 ◁ C3×C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3171 |
735 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C7×C151⋊C5, C3×C7×D151⋊C5, C3×D7×C151⋊C5, … |
| maximal normal subgroup of | C2×C3×C7×C151⋊C5, C3×C7×D151⋊C5, C3×D7×C151⋊C5, … |
| maximal quotient of | C2×C3×C7×C151⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15855, 2);