Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#27134319 |
| Fitting, socle, Hall | C32×C52×C41 ⋊ C22 |
| derived | C3×C52×C41 ⋊ C22×C3 |
| Hall | C52×C41 ⋊ C2×C3×D3 |
| Hall | C32×C41 ⋊ D52 |
| Hall | C32×C52 ⋊ C2×D41 |
| Sylow | C41 ⋊ C3×D15⋊D5 |
| Sylow | C52 ⋊ C2×C3×D123 |
| Sylow | C32 ⋊ (C5⋊D5)⋊D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #27134319 |
| commutator, cosocle, hypocenter | C3×C52×C41 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C41 | C22 |
| LCS | G ▷ C3×C52×C41 | |
| UCS | C1 ◁ C3 | |
224 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1230 |
2610 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 527);