Finite Group DatabasebetaFinite Group Databasebeta| order | 18204 |
| isoclinism | isoclinic class of C3⋊#4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×C3⋊#4223 |
| unambiguous semidirect product | C3⋊(C37×#4223) |
| Fitting, socle, Hall | C3×C37×C41 ⋊ C4 |
| derived, Hall | C3×C41 ⋊ C4×C37 |
| Hall | C37×C41 ⋊ Dic3 |
| Hall | C3×C37 ⋊ #4223 |
| Sylow | C41 ⋊ Dic3×C37 |
| Sylow | C3 ⋊ C37×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C3⋊#4223 |
| commutator, hypocenter | C3×C41 | C4×C37 |
| Frattini | C1 | G |
| Fitting, socle | C3×C37×C41 | C4 |
| prime radical | C3×C37×D41 | C2 |
| cosocle | C3×D41 | C2×C37 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C37 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4551 |
1332 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18204, 31);