Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D31×#90646 |
| derived, Hall | C31×C52⋊C9 ⋊ C22 |
| Hall | C52×C31 ⋊ C2×D9 |
| Hall | C52⋊C9 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×#90646 |
| Sylow | C52 ⋊ D9×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C31×C52⋊C9 | C22 |
| Frattini | C3 | D31×#3874 |
| Fitting, socle | C3×C52×C31 | C2×D3 |
| LCS | G ▷ C31×C52⋊C9 | |
| UCS | C1 | |
100 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 19 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
408 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 253);