Finite Group DatabasebetaFinite Group Databasebeta| order | 1350 |
| isoclinism | isoclinic class of #13062500 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3×C5 |
No aliases for this group.
| Fitting, derived | C32×C52 ⋊ C2×C3 |
| Hall | C32⋊(C52⋊C3) ⋊ C2 |
| Sylow | C52 ⋊ (C3⋊D3)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C52 | C2×C3 |
| Frattini | C3 | C3⋊((C5⋊D5)⋊C3) |
| socle | C3×C52 | C3×D3 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 45 |
Polycyclic presentation:
2,3^3,5^2|c^a=c^2,d^a=d^2,e^a=e^4,f^a=f^4,c^b=cd,e^b=ef,f^b=e^2f^346 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1350, 59);