Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C31 · Schur multiplier (H2) = C5 |
| direct product | C31×#1039⋊C9 |
| unambiguous semidirect product | #1039⋊(C9×C31) |
| derived, Sylow | C52 ⋊ C4×C9×C31 |
| Hall | C31×C52⋊C9 ⋊ C4 |
| Hall | C31×#1039 ⋊ C9 |
| Hall | C52×C31 ⋊ C4×C9 |
| Hall | C52⋊C9 ⋊ C4×C31 |
| Hall | #1039 ⋊ C9×C31 |
60 conjugacy classes of subgroups.
1860 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 105);