Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Hall | C32×C5 ⋊ C2×#41 |
| Sylow | C32 ⋊ C2×#709 |
| Sylow | C5 ⋊ #64312 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D32×D5 |
| commutator, socle, cosocle | C2×C32×C5 | C24 |
| Fitting | C32×C4×C5 | C23 |
| hypercenter | C4 | D32×D5 |
| hypocenter | C32×C5 | C2×#41 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 ◁ C4 | |
710 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 144 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=e,c^2=e,d^2=e,d^a=de,h^a=h^4,g^b=g^2,f^c=f^2117 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#64312, #72231747, #72259815 |
| maximal normal subgroup of | D5×#64312, #72231747, #72259815 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5223);