Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Hall | C32×C5 ⋊ #120 |
| Sylow | C32 ⋊ #4028 |
| Sylow | C5 ⋊ #64162 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D5×C3⋊D3 |
| commutator, socle, cosocle | C22×C32×C5 | C23 |
| Fitting | C23×C32×C5 | C22 |
| hypercenter | C23 | D5×C3⋊D3 |
| hypocenter | C32×C5 | #120 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 ◁ C23 | |
780 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 152 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|b^2=e,b^a=be,h^a=h^4,c^b=cd,f^b=f^2,g^b=g^2162 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#64162, #72230223, C3⋊D3×#4028 |
| maximal normal subgroup of | D5×#64162, #72230223, C3⋊D3×#4028 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 3360);