Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D15×D41 |
| Fitting, socle, Hall | C3×C52×C41 ⋊ C22 |
| derived | C3×C5×C41 ⋊ C22×C5 |
| Hall | C52×C41 ⋊ C2×D3 |
| Hall | C3×C41 ⋊ C2×C5×D5 |
| Hall | C3×C52 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×C5×D15 |
| Sylow | C52 ⋊ D3×D41 |
| Sylow | C3 ⋊ C5×D5×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D15×D41 |
| commutator, cosocle, hypocenter | C3×C5×C41 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C41 | C22 |
| LCS | G ▷ C3×C5×C41 | |
| UCS | C1 ◁ C5 | |
96 conjugacy classes of subgroups.
990 conjugacy classes — view the full character table.
| maximal subgroup of | D41×#90646, C5×D41×D45, D41×C3⋊#3874, … |
| maximal normal subgroup of | C3×C5×D15×D41 |
| maximal quotient of | C5×D41×D45, C3×C5×D15×D41, C5×D123⋊D15, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 154);