Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#16814885⋊C3 |
| unambiguous semidirect product | #16814885⋊C32 |
| unambiguous semidirect product | (C3×#16814885)⋊C3 |
| Fitting, socle | C3×C52×C37 ⋊ C3×C4 |
| derived, Hall | C52×C37 ⋊ C32×C4 |
| Hall | C3×C52×C37⋊C3 ⋊ C4 |
| Hall | #16814885 ⋊ C32 |
| Hall | C3×C37⋊C3 ⋊ #1042 |
| Sylow | C37 ⋊ C32×#1042 |
| Sylow | C52 ⋊ C3×#3866⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16814885⋊C3 |
| commutator, hypocenter | C52×C37 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C37 | C3×C4 |
| prime radical | C3×C5×C5⋊(D37⋊C3) | C2 |
| cosocle | C5×D185 | C2×C32 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 ◁ C3 | |
156 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2220 |
342 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 501);