Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| isoclinism | isoclinic class of D123 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×Dic123 |
| unambiguous semidirect product | C3⋊(C25×Dic41) |
| derived, Hall | C3×C41 ⋊ C4×C25 |
| Hall | C3×C25×C41 ⋊ C4 |
| Hall | C25×C41 ⋊ Dic3 |
| Hall | C3×C25 ⋊ Dic41 |
| Sylow | C41 ⋊ Dic3×C25 |
| Sylow | C3 ⋊ C25×Dic41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C25 | D123 |
| commutator, hypocenter | C3×C41 | C4×C25 |
| Frattini | C2×C5 | C5×D123 |
| Fitting | C2×C3×C25×C41 | C2 |
| socle, prime radical, cosocle | C2×C3×C5×C41 | C2×C5 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C2×C25 | |
36 conjugacy classes of subgroups.
3150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C25×Dic369, C3×C25×Dic123, C25×C3⋊Dic123 |
| maximal normal subgroup of | C3×C25×Dic123 |
| maximal quotient of | C25×Dic369, C3×C25×Dic123, C25×C3⋊Dic123 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 10);