Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C3×C5 |
| direct product | C52×C3⋊D3×D41 |
| Fitting, socle, Hall | C32×C52×C41 ⋊ C22 |
| derived, Hall | C32×C41 ⋊ C22×C52 |
| Hall | C52×C41 ⋊ C2×C3⋊D3 |
| Hall | C32×C52 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×C52×C3⋊D3 |
| Sylow | C32 ⋊ C2×C52×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C3⋊D3×D41 |
| commutator, cosocle, hypocenter | C32×C41 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C41 | C22 |
| LCS | G ▷ C32×C41 | |
| UCS | C1 ◁ C52 | |
480 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9225 |
3300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 567);