Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| isoclinism | isoclinic class of D123 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×Dic123 |
| unambiguous semidirect product | C3⋊(C52×Dic41) |
| derived, Hall | C3×C41 ⋊ C4×C52 |
| Hall | C3×C52×C41 ⋊ C4 |
| Hall | C52×C41 ⋊ Dic3 |
| Hall | C3×C52 ⋊ Dic41 |
| Sylow | C41 ⋊ C52×Dic3 |
| Sylow | C3 ⋊ C52×Dic41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | D123 |
| commutator, hypocenter | C3×C41 | C4×C52 |
| Frattini | C2 | C52×D123 |
| Fitting, socle, prime radical | C2×C3×C52×C41 | C2 |
| cosocle | C2×C3×C41 | C2×C52 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C2×C52 | |
96 conjugacy classes of subgroups.
3150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×Dic369, C52⋊C3×Dic123, C52×C3⋊Dic123, … |
| maximal normal subgroup of | C52⋊C3×Dic123, C3×C52×Dic123 |
| maximal quotient of | C52×Dic369, C52×C3⋊Dic123, C3×C52×Dic123 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 70);