Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×D15×C41⋊C5 |
| unambiguous semidirect product | (C2×C3)⋊(D5×C41⋊C5) |
| unambiguous semidirect product | (C2×C5)⋊(D3×C41⋊C5) |
| unambiguous semidirect product | (C2×D15×C41)⋊C5 |
| Fitting, socle | C2×C3×C5×C41 ⋊ C2×C5 |
| 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 ⋊ C2×C5×D15 |
| Sylow | C3 ⋊ C2×D5×C41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D15×C41⋊C5 |
| commutator, cosocle, hypocenter | C3×C5×C41 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C41 | C2×C5 |
| LCS | G ▷ C3×C5×C41 | |
| UCS | C1 ◁ C2 | |
96 conjugacy classes of subgroups.
234 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D45×C41⋊C5, D3×D15×C41⋊C5, C2×C3×D15×C41⋊C5, … |
| maximal normal subgroup of | C2×C3×D15×C41⋊C5 |
| maximal quotient of | C2×D45×C41⋊C5, D3×D15×C41⋊C5, C2×C3×D15×C41⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 117);