Finite Group DatabasebetaFinite Group Databasebeta| order | 18204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D111⋊D41 |
| unambiguous semidirect product | D123⋊D37 |
| unambiguous semidirect product | D1517⋊D3 |
| Fitting, socle, derived, Hall | C3×C37×C41 ⋊ C22 |
| Hall | C37×C41 ⋊ C2×D3 |
| Hall | C3×C41 ⋊ C2×D37 |
| Hall | C3×C37 ⋊ C2×D41 |
| Sylow | C41 ⋊ D3×D37 |
| Sylow | C37 ⋊ D3×D41 |
| Sylow | C3 ⋊ D37×D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C37×C41 | C22 |
| LCS | G ▷ C3×C37×C41 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4551 |
Polycyclic presentation:
2^2,3,37,41|d^a=d^36,e^a=e^40,c^b=c^2,d^b=d^361200 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18204, 42);