Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#24926250 |
| Fitting, derived, Hall | C3×C25×C109 ⋊ C4 |
| Hall | C25×C109 ⋊ Dic3 |
| Hall | C3×C109 ⋊ Dic25 |
| Sylow | C109 ⋊ Dic75 |
| Hall | C3×C25 ⋊ #89137 |
| Sylow | C25 ⋊ C3⋊#89137 |
| Sylow | C3 ⋊ #24926250 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C25×C109 | C4 |
| Frattini | C5 | C3⋊#14546129 |
| socle | C3×C5×C109 | Dic5 |
| prime radical | C3×C5×D109 | D5 |
| cosocle | C3×C25×D109 | C2 |
| LCS | G ▷ C3×C25×C109 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8175 |
Polycyclic presentation:
2^2,3,5,109,5|a^2=b,d^5=f^4,c^a=c^2,d^a=d^4f,e^a=e^76,f^a=f^4,e^b=e^1082103 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 37);