Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| Fitting, socle | C3×C52×C31 ⋊ C22×C3 |
| derived, Hall | C52×C31 ⋊ C22×C32 |
| Hall | C3×C52×C31⋊C3 ⋊ C22 |
| Hall | D5×D155 ⋊ C32 |
| Hall | C3×C31⋊C3 ⋊ D52 |
| Sylow | C31 ⋊ C32×D52 |
| Sylow | C52 ⋊ C2×C3×D31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5×C5⋊(D31⋊C3) |
| commutator, cosocle, hypocenter | C52×C31 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C31 | C22×C3 |
| LCS | G ▷ C52×C31 | |
| UCS | C1 ◁ C3 | |
288 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
444 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 505);