Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | D5×C3⋊(D41⋊C5) |
| unambiguous semidirect product | (C3×D5)⋊(D41⋊C5) |
| unambiguous semidirect product | (D5×C41⋊C5)⋊D3 |
| unambiguous semidirect product | (D5×D123)⋊C5 |
| Fitting, socle, derived | C3×C5×C41 ⋊ C22×C5 |
| Hall | C3×C5×C41⋊C5 ⋊ C22 |
| Hall | C5×C41⋊C5 ⋊ C2×D3 |
| Hall | C3×C41 ⋊ C2×C5×D5 |
| Sylow | C41 ⋊ C5×D3×D5 |
| Sylow | C3 ⋊ D5×D41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C41 | C22×C5 |
| LCS | G ▷ C3×C5×C41 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
108 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C9⋊(D41⋊C5), C3×D5×C3⋊(D41⋊C5), D15×C3⋊(D41⋊C5), … |
| maximal normal subgroup of | C3×D5×C3⋊(D41⋊C5) |
| maximal quotient of | D5×C9⋊(D41⋊C5), C3×D5×C3⋊(D41⋊C5), D15×C3⋊(D41⋊C5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 91);