Finite Group DatabasebetaFinite Group Databasebeta| order | 10380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C3⋊#10621924 |
| unambiguous semidirect product | C3⋊(C5×#10621924) |
| Fitting, socle, Hall | C3×C5×C173 ⋊ C4 |
| derived, Hall | C3×C173 ⋊ C4×C5 |
| Hall | C5×C173 ⋊ Dic3 |
| Sylow | C173 ⋊ C5×Dic3 |
| Hall | C3×C5 ⋊ #10621924 |
| Sylow | C3 ⋊ C5×#10621924 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊#10621924 |
| commutator, hypocenter | C3×C173 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C173 | C4 |
| prime radical | C3×C5×D173 | C2 |
| cosocle | C3×D173 | C2×C5 |
| LCS | G ▷ C3×C173 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
675 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C9⋊#10621924, C3×C5×C3⋊#10621924, C5×C3⋊(C3⋊#10621924) |
| maximal normal subgroup of | C3×C5×C3⋊#10621924 |
| maximal quotient of | C5×C9⋊#10621924, C3×C5×C3⋊#10621924, C5×C3⋊(C3⋊#10621924) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10380, 17);