Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×C3⋊(#3866⋊C3) |
| unambiguous semidirect product | C3⋊(C52×#3866⋊C3) |
| unambiguous semidirect product | (C3⋊#3866)⋊(C3×C52) |
| unambiguous semidirect product | (C5×C3⋊#3866)⋊(C3×C5) |
| Fitting, socle | C3×C52×C37 ⋊ C3×C4 |
| derived | C3×C37 ⋊ C3×C4×C52 |
| Hall | C3×C52×C37⋊C3 ⋊ C4 |
| Hall | C52×C37 ⋊ C3×Dic3 |
| Hall | C3×C37⋊C3 ⋊ C4×C52 |
| Sylow | C37 ⋊ C3×C52×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C3⋊(#3866⋊C3) |
| commutator, hypocenter | C3×C37 | C3×C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C37 | C3×C4 |
| prime radical | C3×C52×D37⋊C3 | C2 |
| cosocle | C3×D37 | C2×C3×C52 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C52 | |
224 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2775 |
675 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 556);