Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52×C9 · Schur multiplier (H2) = C5 |
| direct product | C52×AGL(1,𝔽37) |
| Fitting, socle, Hall | C52×C37 ⋊ C4×C9 |
| derived, Sylow | C37 ⋊ C4×C52×C9 |
| Hall | C52×#66526 ⋊ C4 |
| Hall | C52×#3866 ⋊ C9 |
| Hall | #66526 ⋊ C4×C52 |
| Hall | #3866 ⋊ C52×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | AGL(1,𝔽37) |
| commutator, hypocenter | C37 | C4×C52×C9 |
| Frattini | C1 | G |
| Fitting, socle | C52×C37 | C4×C9 |
| prime radical | C52×D37⋊C3 | C2×C3 |
| cosocle | D37⋊C3 | C2×C3×C52 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C52 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 925 |
925 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 435);