Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊D2325 |
| unambiguous semidirect product | (C2×C3)⋊D2325 |
| unambiguous semidirect product | (C2×C25)⋊(C3⋊D93) |
| unambiguous semidirect product | (C2×C31)⋊(C3⋊D75) |
| Fitting | C2×C32×C25×C31 ⋊ C2 |
| derived, Hall | C32×C25×C31 ⋊ C22 |
| Hall | C25×C31 ⋊ C2×C3⋊D3 |
| Hall | C32×C31 ⋊ C2×D25 |
| Hall | C32×C25 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×C3⋊D75 |
| Sylow | C25 ⋊ C2×C3⋊D93 |
| Sylow | C32 ⋊ C2×D775 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D2325 |
| commutator, cosocle, hypocenter | C32×C25×C31 | C22 |
| Frattini | C5 | C2×C3⋊D465 |
| Fitting | C2×C32×C25×C31 | C2 |
| socle | C2×C32×C5×C31 | D5 |
| LCS | G ▷ C32×C25×C31 | |
| UCS | C1 ◁ C2 | |
180 conjugacy classes of subgroups.
6978 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 205);