Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C2×C32×C4×C5 ⋊ C4 |
| Hall | C32×C5 ⋊ #95 |
| Sylow | C32 ⋊ (C2×AGL(1,𝔽5))⋊C4 |
| Sylow | C5 ⋊ #63658 |
456 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^5,3^2,5|a^2=c,b^2=d,b^a=be,f^a=f^2,g^a=g^2,h^a=h^2,h^c=h^4156 conjugacy classes — view the full character table.
| maximal subgroup of | #72229915, #72229993, C22⋊C4×C3⋊ΓL(1,𝔽16), … |
| maximal normal subgroup of | #72229915, #72229993, C22⋊C4×C3⋊ΓL(1,𝔽16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2625);