Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Fitting | C2×C32×C5×Q8 ⋊ C2 |
| Hall | C32×C5 ⋊ 2−1+4 |
| Sylow | C32 ⋊ #4147 |
| Sylow | C5 ⋊ #64364 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×C3⋊D15 |
| commutator, socle, cosocle | C2×C32×C5 | C24 |
| Fitting | C2×C32×C5×Q8 | C2 |
| hypercenter | C2×Q8 | C3⋊D15 |
| hypocenter | C32×C5 | 2−1+4 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 ◁ C2×Q8 | |
876 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 876 conjugacy classes of subgroups — too many to draw. Only its 255 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 720 |
Polycyclic presentation:
2^5,3^2,5|b^2=e,c^2=e,d^a=de,f^a=f^2,g^a=g^2,h^a=h^4,c^b=ce237 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5829);