Finite Group DatabasebetaFinite Group Databasebeta| order | 5595 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C373⋊C3 |
| unambiguous semidirect product | C373⋊(C3×C5) |
| unambiguous semidirect product | (C5×C373)⋊C3 |
| Fitting, socle, Hall | C5×C373 ⋊ C3 |
| derived, Sylow | C373 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C373⋊C3 |
| commutator, hypocenter | C373 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C373 | C3 |
| LCS | G ▷ C373 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
635 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C5×C373⋊C3, C5×D373⋊C3, D5×C373⋊C3, … |
| maximal normal subgroup of | C2×C5×C373⋊C3, C5×D373⋊C3, D5×C373⋊C3, … |
| maximal quotient of | C2×C5×C373⋊C3, C5×C373⋊C9, C3×C5×C373⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5595, 1);