Finite Group DatabasebetaFinite Group Databasebeta| order | 18180 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊D3)⋊(D101⋊C5) |
| unambiguous semidirect product | (C3⋊(D101⋊C5))⋊D3 |
| unambiguous semidirect product | ((C3⋊D3)⋊D101)⋊C5 |
| Fitting, socle, derived, Hall | C32×C101 ⋊ C22×C5 |
| Hall | C32×C101⋊C5 ⋊ C22 |
| Hall | (C3⋊D3)⋊D101 ⋊ C5 |
| Hall | C101⋊C5 ⋊ D32 |
| Sylow | C101 ⋊ C5×D32 |
| Sylow | C32 ⋊ C2×D101⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C101 | C22×C5 |
| LCS | G ▷ C32×C101 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 606 |
Polycyclic presentation:
2^2,5,3^2,101|e^a=e^2,f^a=f^100,d^b=d^2,e^b=e^2,f^c=f^95105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18180, 74);