Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| isoclinism | isoclinic class of D93 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C3×C52×Dic93 |
| unambiguous semidirect product | C3⋊(C3×C52×Dic31) |
| derived | C3×C31 ⋊ C3×C4×C52 |
| Hall | C32×C52×C31 ⋊ C4 |
| Hall | C52×C31 ⋊ C3×Dic3 |
| Hall | C32×C31 ⋊ C4×C52 |
| Hall | C32×C52 ⋊ Dic31 |
| Sylow | C31 ⋊ C3×C52×Dic3 |
| Sylow | C32 ⋊ C52×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C52 | D93 |
| commutator, hypocenter | C3×C31 | C3×C4×C52 |
| Frattini | C2 | C3×C52×D93 |
| Fitting, socle, prime radical | C2×C32×C52×C31 | C2 |
| cosocle | C2×C3×C31 | C2×C3×C52 |
| LCS | G ▷ C3×C31 | |
| UCS | C1 ◁ C2×C3×C52 | |
224 conjugacy classes of subgroups.
7200 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 409);