Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C41 · Schur multiplier (H2) = C1 |
| direct product | C5×C41×Dic15 |
| unambiguous semidirect product | C3⋊(C5×Dic5×C41) |
| derived | C3×C5 ⋊ C4×C5×C41 |
| Hall | C3×C52×C41 ⋊ C4 |
| Hall | C52×C41 ⋊ Dic3 |
| Hall | C3×C41 ⋊ C5×Dic5 |
| Hall | C3×C52 ⋊ C4×C41 |
| Sylow | C52 ⋊ Dic3×C41 |
| Sylow | C3 ⋊ C5×Dic5×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C41 | D15 |
| commutator, hypocenter | C3×C5 | C4×C5×C41 |
| Frattini | C2 | C5×D15×C41 |
| Fitting, socle, prime radical | C2×C3×C52×C41 | C2 |
| cosocle | C2×C3×C5 | C2×C5×C41 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C5×C41 | |
64 conjugacy classes of subgroups.
3690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#11744607, C5×C41×Dic45, C41×C3⋊#64470, … |
| maximal normal subgroup of | C3×C5×C41×Dic15 |
| maximal quotient of | C5×C41×Dic45, C5×C41×C3⋊Dic15, C3×C5×C41×Dic15 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 71);