Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C37 · Schur multiplier (H2) = C3 |
| direct product | C3×C37×#1043⋊C3 |
| unambiguous semidirect product | #1043⋊(C32×C37) |
| unambiguous semidirect product | (C3×#1043)⋊(C3×C37) |
| Fitting, socle | C3×C52×C37 ⋊ C3×C4 |
| derived, Sylow | C52 ⋊ C32×C4×C37 |
| Hall | C3×C37×C52⋊C3 ⋊ C4 |
| Hall | C37×#1043 ⋊ C32 |
| Hall | C52×C37 ⋊ C32×C4 |
| Hall | C3×C52⋊C3 ⋊ C4×C37 |
| Hall | #1043 ⋊ C32×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C37 | #1043⋊C3 |
| commutator, hypocenter | C52 | C32×C4×C37 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C37 | C3×C4 |
| prime radical | C3×C37×(C5⋊D5)⋊C3 | C2 |
| cosocle | C5⋊D5 | C2×C32×C37 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3×C37 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1665 |
1554 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 482);