Finite Group DatabasebetaFinite Group Databasebeta| order | 18180 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D45⋊D101 |
| unambiguous semidirect product | D505⋊D9 |
| unambiguous semidirect product | D909⋊D5 |
| Fitting, derived, Hall | C5×C9×C101 ⋊ C22 |
| Hall | C9×C101 ⋊ C2×D5 |
| Hall | C5×C101 ⋊ C2×D9 |
| Sylow | C101 ⋊ D5×D9 |
| Hall | C5×C9 ⋊ C2×D101 |
| Sylow | C9 ⋊ D5×D101 |
| Sylow | C5 ⋊ D9×D101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C9×C101 | C22 |
| Frattini | C3 | D15⋊D101 |
| socle | C3×C5×C101 | C2×D3 |
| LCS | G ▷ C5×C9×C101 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4545 |
Polycyclic presentation:
2^2,3,5,101,3|c^3=f^2,d^a=d^4,e^a=e^100,c^b=c^2f,d^b=d^4,f^b=f^21224 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18180, 40);