Finite Group DatabasebetaFinite Group Databasebeta| order | 10380 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C173 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D3×C173 |
| unambiguous semidirect product | C3⋊(C22×C5×C173) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C5×C173) |
| Fitting, socle | C2×C3×C5×C173 ⋊ C2 |
| derived, Sylow | C3 ⋊ C22×C5×C173 |
| Hall | C3×C5×C173 ⋊ C22 |
| Hall | C3×C173 ⋊ C22×C5 |
| Hall | C3×C5 ⋊ C22×C173 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C173 | D3 |
| commutator, cosocle, hypocenter | C3 | C22×C5×C173 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C173 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C5×C173 | |
40 conjugacy classes of subgroups.
5190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×D9×C173, C5×D32×C173, C2×C3×C5×D3×C173, … |
| maximal normal subgroup of | C2×C3×C5×D3×C173 |
| maximal quotient of | C2×C5×D9×C173, C5×D32×C173, C2×C3×C5×D3×C173, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10380, 33);