Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C52×D3×D93 |
| unambiguous semidirect product | (C3×D3)⋊(C52×D31) |
| Fitting, socle, Hall | C32×C52×C31 ⋊ C22 |
| derived, Hall | C32×C31 ⋊ C22×C52 |
| Hall | C52×C31 ⋊ D32 |
| Hall | C32×C52 ⋊ C2×D31 |
| Sylow | C31 ⋊ C52×D32 |
| Sylow | C32 ⋊ C2×C52×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D3×D93 |
| commutator, cosocle, hypocenter | C32×C31 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C31 | C22 |
| LCS | G ▷ C32×C31 | |
| UCS | C1 ◁ C52 | |
352 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
3600 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 671);