Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | Dic109⋊(C52⋊C3) |
| derived, Hall | C52×C109 ⋊ C3×C4 |
| Hall | C52×Dic109 ⋊ C3 |
| Hall | C52⋊(C109⋊C3) ⋊ C4 |
| Hall | Dic109 ⋊ C52⋊C3 |
| Sylow | C109 ⋊ C4×C52⋊C3 |
| Sylow | C52 ⋊ Dic109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D109⋊(C52⋊C3) |
| commutator, hypocenter | C52×C109 | C3×C4 |
| Fitting, socle, cosocle | C2×C52×C109 | C2×C3 |
| prime radical | C2×C52⋊(C109⋊C3) | C2 |
| LCS | G ▷ C52×C109 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6540 |
Polycyclic presentation:
2,3,5^2,109,2|a^2=f,e^a=e^108,c^b=c^3d^2,d^b=cd,e^b=e^63944 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 65);