Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊#24926275 |
| Fitting, socle, derived, Hall | C3×C52×C109 ⋊ C4 |
| Hall | C52×C109 ⋊ Dic3 |
| Hall | C3×C109 ⋊ #1044 |
| Sylow | C109 ⋊ C3⋊#1044 |
| Hall | C3×C52 ⋊ Dic109 |
| Sylow | C52 ⋊ Dic327 |
| Sylow | C3 ⋊ #24926275 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C109 | C4 |
| prime radical, cosocle | C3×C5⋊D5×C109 | C2 |
| LCS | G ▷ C3×C52×C109 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3270 |
Polycyclic presentation:
2^2,3,5^2,109|a^2=b,c^a=c^2,d^a=d^2,e^a=e^3,f^a=f^108,d^b=d^4,e^b=e^42292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 198);