Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊#16861527 |
| unambiguous semidirect product | C3⋊(C3×#16861527) |
| Fitting, socle, Hall | C32×C52×C41 ⋊ C4 |
| derived | C3×C52×C41 ⋊ C3×C4 |
| Hall | C52×C41 ⋊ C3×Dic3 |
| Hall | C32×C41 ⋊ #1042 |
| Hall | C32×C52 ⋊ Dic41 |
| Sylow | C41 ⋊ C3×C3⋊#1042 |
| Sylow | C52 ⋊ C3×Dic123 |
| Sylow | C32 ⋊ #16861527 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊#16861527 |
| commutator, hypocenter | C3×C52×C41 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C41 | C4 |
| prime radical | C32×C5×D5×C41 | C2 |
| cosocle | C3×C5×D5×C41 | C2×C3 |
| LCS | G ▷ C3×C52×C41 | |
| UCS | C1 ◁ C3 | |
124 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 124 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) = 2460 |
3699 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 521);