Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3 |
| direct product | C32×C5×#10625193 |
| Fitting, socle, Hall | C32×C52×C37 ⋊ C4 |
| derived | C5×C37 ⋊ C32×C4×C5 |
| Hall | C52×C37 ⋊ C32×C4 |
| Hall | C32×C37 ⋊ C5×AGL(1,𝔽5) |
| Hall | C32×C52 ⋊ Dic37 |
| Sylow | C37 ⋊ C32×C5×AGL(1,𝔽5) |
| Sylow | C52 ⋊ C32×Dic37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5 | #10625193 |
| commutator, hypocenter | C5×C37 | C32×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C37 | C4 |
| prime radical | C32×C5×D5×C37 | C2 |
| cosocle | D5×C37 | C2×C32×C5 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 ◁ C32×C5 | |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6660 |
3465 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 662);