Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C37⋊C3×C3⋊#1043 |
| unambiguous semidirect product | C3⋊(#1043×C37⋊C3) |
| Fitting, socle, derived | C3×C52×C37 ⋊ C3×C4 |
| Hall | C3×C52×C37⋊C3 ⋊ C4 |
| Hall | C52×C37 ⋊ C3×Dic3 |
| Hall | C3×C37⋊C3 ⋊ #1043 |
| Sylow | C37 ⋊ C3×C3⋊#1043 |
| Sylow | C52 ⋊ Dic3×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C37 | C3×C4 |
| prime radical | C3×C5⋊D5×C37⋊C3 | C2 |
| cosocle | C3×C37×C5⋊D5 | C2×C3 |
| LCS | G ▷ C3×C52×C37 | |
| UCS | C1 | |
224 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2775 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 588);