Finite Group DatabasebetaFinite Group Databasebeta| order | 1815 |
| isoclinism | isoclinic class of #10597243 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×#10597243 |
| Fitting, socle, Hall | C3×C112 ⋊ C5 |
| derived, Sylow | C112 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #10597243 |
| commutator, cosocle, hypocenter | C112 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C112 | C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 363 |
87 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1815, 5);