Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×C3⋊Dic465 |
| unambiguous semidirect product | C3⋊(C5×Dic465) |
| derived | C32×C5×C31 ⋊ C4×C5 |
| Hall | C32×C52×C31 ⋊ C4 |
| Hall | C52×C31 ⋊ C3⋊Dic3 |
| Hall | C32×C31 ⋊ C5×Dic5 |
| Hall | C32×C52 ⋊ Dic31 |
| Sylow | C31 ⋊ C5×C3⋊Dic15 |
| Sylow | C52 ⋊ C3⋊Dic93 |
| Sylow | C32 ⋊ C5×Dic155 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C3⋊D465 |
| commutator, hypocenter | C32×C5×C31 | C4×C5 |
| Frattini | C2 | C5×C3⋊D465 |
| Fitting, socle, prime radical | C2×C32×C52×C31 | C2 |
| cosocle | C2×C32×C5×C31 | C2×C5 |
| LCS | G ▷ C32×C5×C31 | |
| UCS | C1 ◁ C2×C5 | |
192 conjugacy classes of subgroups.
6990 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 401);