Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5×C41 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×Dic5×C41 |
| derived | C5 ⋊ C3×C4×C5×C41 |
| Hall | C3×C52×C41 ⋊ C4 |
| Hall | C52×C41 ⋊ C3×C4 |
| Hall | C3×C52 ⋊ C4×C41 |
| Sylow | C52 ⋊ C3×C4×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5×C41 | D5 |
| commutator, hypocenter | C5 | C3×C4×C5×C41 |
| Frattini | C2 | C3×C5×D5×C41 |
| Fitting, socle, prime radical | C2×C3×C52×C41 | C2 |
| cosocle | C2×C5 | C2×C3×C5×C41 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C3×C5×C41 | |
64 conjugacy classes of subgroups.
4920 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C9×Dic5×C41, C3×C41×#64470, C3×C5×C41×Dic15, … |
| maximal normal subgroup of | C5×C9×Dic5×C41, C32×C5×Dic5×C41 |
| maximal quotient of | C5×C9×Dic5×C41, C3×C5×C41×Dic15, C32×C5×Dic5×C41 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 65);