Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C32×C5 ⋊ #117 |
| Sylow | C32 ⋊ #4018 |
| Sylow | C5 ⋊ #63957 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D32×D5 |
| commutator | C2×C32×C5 | C22×C4 |
| Fitting, socle, cosocle | C22×C32×C5 | C23 |
| prime radical | C22×C32×D5 | C22 |
| hypocenter | C32×C5 | #117 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
358 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^5,3^2,5|b^2=d,c^2=de,b^a=be,c^a=ce,h^a=h^4,f^b=f^2,g^c=g^2120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2204);