Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3×C5 |
| direct product | D37×C3⋊(C3⋊(C5⋊D5)) |
| unambiguous semidirect product | (C3×D37)⋊(C3⋊(C5⋊D5)) |
| unambiguous semidirect product | (C5×D37)⋊(C3⋊D15) |
| Fitting, socle, derived, Hall | C32×C52×C37 ⋊ C22 |
| Hall | C52×C37 ⋊ C2×C3⋊D3 |
| Hall | C32×C37 ⋊ C2×C5⋊D5 |
| Hall | C32×C52 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×C3⋊(C3⋊(C5⋊D5)) |
| Sylow | C52 ⋊ C3⋊D3×D37 |
| Sylow | C32 ⋊ C5⋊D5×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C52×C37 | C22 |
| LCS | G ▷ C32×C52×C37 | |
| UCS | C1 | |
480 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8325 |
2280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 763);