Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of #14268459 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting, socle, Hall | C32×C52 ⋊ D4 |
| Sylow | C52 ⋊ C4⋊(C3⋊D3) |
| Sylow | C32 ⋊ D52⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C32×C5⋊D5 | C22 |
| Fitting, socle, hypocenter | C32×C52 | D4 |
| LCS | G ▷ C32×C5⋊D5 ▷ C32×C52 | |
| UCS | C1 | |
174 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
Polycyclic presentation:
2^3,3^2,5^2|b^2=c,b^a=bc,d^a=d^2,e^a=e^2,f^a=g,g^a=f,f^b=f^3,g^b=g^2,f^c=f^4,g^c=g^454 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 653);