Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of #14268076 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C52⋊C9 ⋊ C8 |
| Sylow | C52 ⋊ C9⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C52⋊C9 | C8 |
| Frattini | C3 | #10597167 |
| Fitting, socle | C3×C52 | C3⋊C8 |
| prime radical | C3×C5⋊D5 | Dic3 |
| cosocle | #1043⋊C9 | C2 |
| LCS | G ▷ C52⋊C9 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 90 |
Polycyclic presentation:
2^3,3^2,5^2|a^2=b,b^2=c,d^3=e,d^a=d^2e^2,e^a=e^2,f^a=f^4g^2,g^a=f^3g,f^b=f^2,g^b=g^2,f^c=f^4,g^c=g^4,f^d=g,g^d=f^4g^427 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 270);