Finite Group DatabasebetaFinite Group Databasebeta| order | 36108 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D153⋊D59 |
| unambiguous semidirect product | D531⋊D17 |
| unambiguous semidirect product | D1003⋊D9 |
| Fitting, derived, Hall | C9×C17×C59 ⋊ C22 |
| Hall | C17×C59 ⋊ C2×D9 |
| Hall | C9×C59 ⋊ C2×D17 |
| Hall | C9×C17 ⋊ C2×D59 |
| Sylow | C59 ⋊ D9×D17 |
| Sylow | C17 ⋊ D9×D59 |
| Sylow | C9 ⋊ D17×D59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C17×C59 | C22 |
| Frattini | C3 | D51⋊D59 |
| socle | C3×C17×C59 | C2×D3 |
| LCS | G ▷ C9×C17×C59 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9027 |
Polycyclic presentation:
2^2,3,17,59,3|c^3=f^2,d^a=d^16,e^a=e^58,c^b=c^2f,d^b=d^16,f^b=f^22322 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36108, 20);