Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of #13108537 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C34 |
No aliases for this group.
| Fitting, socle, derived, Hall | C34×C5 ⋊ C4 |
| Sylow | C34 ⋊ Dic5 |
| Sylow | C5 ⋊ #66472 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C34×C5 | C4 |
| prime radical, cosocle | C5×C3⋊(C3⋊(C3⋊D3)) | C2 |
| LCS | G ▷ C34×C5 | |
| UCS | C1 | |
472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
Polycyclic presentation:
2^2,3^4,5|a^2=b,c^a=cd^2,d^a=c^2d^2,e^a=ef^2,f^a=e^2f^2,g^a=g^4,c^b=c^2,d^b=d^2,e^b=e^2,f^b=f^2108 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#66472, #72269601, #72269605, … |
| maximal normal subgroup of | D5×#66472, #72269601, #72269605, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 443);