Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Hall | C32×C25 ⋊ D4 |
| Sylow | C25 ⋊ #638 |
| Sylow | C32 ⋊ D100 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D3×D25 |
| commutator, Fitting, cosocle | C2×C32×C25 | C22 |
| Frattini | C2×C5 | D5×C3⋊D3 |
| socle | C2×C32×C5 | C2×D5 |
| hypocenter | C32×C25 | D4 |
| LCS | G ▷ C2×C32×C25 ▷ C32×C25 | |
| UCS | C1 ◁ C2 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 900 |
Polycyclic presentation:
2^3,3^2,5^2|b^2=c,f^5=g,b^a=bc,f^a=f^4g^4,g^a=g^4,d^b=d^2,e^b=e^2165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 76);