Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Hall | C32×C5 ⋊ #97 |
| Sylow | C32 ⋊ #3992 |
| Sylow | C5 ⋊ #63767 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽5)×#157 |
| commutator, Fitting, socle | C2×C32×C5 | C42 |
| prime radical | C2×C3⋊D15 | C2×C4 |
| cosocle | #67137 | C22 |
| hypocenter | C32×C5 | #97 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 | |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^5,3^2,5|a^2=c,b^2=d,c^2=e,d^2=e,b^a=be,h^a=h^2,f^b=fg,g^b=fg^2,h^c=h^4,f^d=f^2,g^d=g^248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4663);