Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| isoclinism | isoclinic class of C3⋊D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C31×C3⋊D75 |
| unambiguous semidirect product | (C2×C3)⋊(C31×D75) |
| unambiguous semidirect product | (C2×C25)⋊(C3⋊D3×C31) |
| Fitting | C2×C32×C25×C31 ⋊ C2 |
| derived, Hall | C32×C25 ⋊ C22×C31 |
| Hall | C32×C25×C31 ⋊ C22 |
| Hall | C25×C31 ⋊ C2×C3⋊D3 |
| Hall | C32×C31 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×C3⋊D3×C31 |
| Sylow | C32 ⋊ C2×C31×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C31 | C3⋊D75 |
| commutator, cosocle, hypocenter | C32×C25 | C22×C31 |
| Frattini | C5 | C2×C31×C3⋊D15 |
| Fitting | C2×C32×C25×C31 | C2 |
| socle | C2×C32×C5×C31 | D5 |
| LCS | G ▷ C32×C25 | |
| UCS | C1 ◁ C2×C31 | |
180 conjugacy classes of subgroups.
7068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 206);