Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D5×D205 |
| unambiguous semidirect product | (C5×D5)⋊(C3×D41) |
| unambiguous semidirect product | (D5×C41)⋊(C3×D5) |
| Fitting, socle, Hall | C3×C52×C41 ⋊ C22 |
| derived, Hall | C52×C41 ⋊ C22×C3 |
| Hall | C3×C41 ⋊ D52 |
| Hall | C3×C52 ⋊ C2×D41 |
| Sylow | C41 ⋊ C3×D52 |
| Sylow | C52 ⋊ C2×C3×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5×D205 |
| commutator, cosocle, hypocenter | C52×C41 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C41 | C22 |
| LCS | G ▷ C52×C41 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
1248 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×D5×D205, C3×#3874⋊D41, C32×D5×D205, … |
| maximal normal subgroup of | C9×D5×D205, C32×D5×D205 |
| maximal quotient of | C9×D5×D205, C32×D5×D205, C3×D5×D615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 145);