Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| Fitting | C3×C25×C31 ⋊ C22×C3 |
| derived, Hall | C25×C31 ⋊ C22×C32 |
| Hall | C3×C25×C31⋊C3 ⋊ C22 |
| Hall | D25×D31 ⋊ C32 |
| Hall | C3×C31⋊C3 ⋊ C2×D25 |
| Sylow | C31 ⋊ C2×C32×D25 |
| Sylow | C25 ⋊ C2×C3×D31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D25×D31⋊C3 |
| commutator, cosocle, hypocenter | C25×C31 | C22×C32 |
| Frattini | C5 | C3×D5×D31⋊C3 |
| Fitting | C3×C25×C31 | C22×C3 |
| socle | C3×C5×C31 | C2×C3×D5 |
| LCS | G ▷ C25×C31 | |
| UCS | C1 ◁ C3 | |
180 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
462 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 144);