Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C32×C5 ⋊ C4⋊Q8 |
| Sylow | C32 ⋊ #4015 |
| Sylow | C5 ⋊ #63840 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D32×D5 |
| commutator, Fitting, socle, prime radical, cosocle | C22×C32×C5 | C23 |
| hypocenter | C32×C5 | C4⋊Q8 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
310 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^5,3^2,5|a^2=e,b^2=d,c^2=de,b^a=bd,c^a=cde,h^a=h^4,f^b=f^2,g^c=g^2114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2520);