Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C32×C5 ⋊ #95 |
| Sylow | C32 ⋊ #3963 |
| Sylow | C5 ⋊ #63579 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C23 | D3×D15 |
| commutator | C2×C32×C5 | C42 |
| Fitting, socle, prime radical, cosocle | C23×C32×C5 | C22 |
| hypocenter | C32×C5 | #95 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C23 | |
358 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^5,3^2,5|a^2=e,b^2=c,b^a=bd,f^a=f^2,h^a=h^4,g^b=g^2204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1187);