Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| isoclinism | isoclinic class of D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×Dic75 |
| unambiguous semidirect product | C3⋊(C41×Dic25) |
| derived, Hall | C3×C25 ⋊ C4×C41 |
| Hall | C3×C25×C41 ⋊ C4 |
| Hall | C25×C41 ⋊ Dic3 |
| Hall | C3×C41 ⋊ Dic25 |
| Sylow | C25 ⋊ Dic3×C41 |
| Sylow | C3 ⋊ C41×Dic25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C41 | D75 |
| commutator, hypocenter | C3×C25 | C4×C41 |
| Frattini | C2×C5 | D15×C41 |
| Fitting | C2×C3×C25×C41 | C2 |
| socle, prime radical | C2×C3×C5×C41 | D5 |
| cosocle | C2×C3×C25 | C2×C41 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C2×C41 | |
36 conjugacy classes of subgroups.
3198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×Dic225, C3×C41×Dic75, C41×C3⋊Dic75 |
| maximal normal subgroup of | C3×C41×Dic75 |
| maximal quotient of | C41×Dic225, C3×C41×Dic75, C41×C3⋊Dic75 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 11);