Finite Group DatabasebetaFinite Group Databasebeta| order | 10380 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#16812337 |
| Fitting, socle, Hall | C3×C5×C173 ⋊ C4 |
| derived, Hall | C5×C173 ⋊ C3×C4 |
| Hall | C3×C173 ⋊ AGL(1,𝔽5) |
| Sylow | C173 ⋊ C3×AGL(1,𝔽5) |
| Hall | C3×C5 ⋊ #10621924 |
| Sylow | C5 ⋊ C3×#10621924 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16812337 |
| commutator, hypocenter | C5×C173 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C173 | C4 |
| prime radical | C3×D865 | C2 |
| cosocle | D865 | C2×C3 |
| LCS | G ▷ C5×C173 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
660 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#16812337, C32×#16812337, C3×C3⋊#16812337 |
| maximal normal subgroup of | C9×#16812337, C32×#16812337 |
| maximal quotient of | C9×#16812337, C32×#16812337, C3×C3⋊#16812337 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10380, 12);