Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C32×C5 ⋊ C2×M16 |
| Sylow | C32 ⋊ D5×M16 |
| Sylow | C5 ⋊ #63818 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D32×D5 |
| commutator, socle | C2×C32×C5 | C22×C4 |
| Fitting, cosocle | C32×C4×C5 | C23 |
| prime radical | C2×D5×C3⋊D3 | C4 |
| hypocenter | C32×C5 | C2×M16 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C4 | |
326 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^5,3^2,5|b^2=d,c^2=d,d^2=e,b^a=be,c^a=ce,h^a=h^4,c^b=ce,f^b=f^2,g^c=g^2108 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#63818, #72230425, #72231218 |
| maximal normal subgroup of | D5×#63818, #72230425 |
| maximal quotient of | #72231218 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1960);