Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C37⋊C3×C3⋊#1042 |
| unambiguous semidirect product | C3⋊(#1042×C37⋊C3) |
| unambiguous semidirect product | (C37×C3⋊#1042)⋊C3 |
| Fitting, socle, derived | C3×C52×C37 ⋊ C3×C4 |
| Hall | C3×C52×C37⋊C3 ⋊ C4 |
| Hall | C52×C37 ⋊ C3×Dic3 |
| Hall | C3×C37⋊C3 ⋊ #1042 |
| Sylow | C37 ⋊ C3×C3⋊#1042 |
| 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×C5×D5×C37 | C2×C3 |
| LCS | G ▷ C3×C52×C37 | |
| UCS | C1 | |
124 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2220 |
495 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 571);