Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C11 |
| direct product | D3×C11⋊D275 |
| unambiguous semidirect product | (D3×C11)⋊D275 |
| unambiguous semidirect product | (D3×C25)⋊(C11⋊D11) |
| Fitting, derived, Hall | C3×C112×C25 ⋊ C22 |
| Hall | C112×C25 ⋊ C2×D3 |
| Hall | C3×C112 ⋊ C2×D25 |
| Sylow | C112 ⋊ D3×D25 |
| Hall | C3×C25 ⋊ C2×C11⋊D11 |
| Sylow | C25 ⋊ D3×C11⋊D11 |
| Sylow | C3 ⋊ C2×C11⋊D275 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C112×C25 | C22 |
| Frattini | C5 | D3×C5⋊(C11⋊D11) |
| socle | C3×C5×C112 | C2×D5 |
| LCS | G ▷ C3×C112×C25 | |
| UCS | C1 | |
420 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9075 |
4542 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 327);