Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D32⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C32×C5 ⋊ #95 |
| Sylow | C32 ⋊ #3963 |
| Sylow | C5 ⋊ #63737 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D32⋊D5 |
| commutator | C5×C3⋊D3 | C42 |
| Fitting, socle | C22×C32×C5 | D4 |
| prime radical, cosocle | C22×C5×C3⋊D3 | C22 |
| hypocenter | C32×C5 | #95 |
| LCS | G ▷ C5×C3⋊D3 ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
260 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 55 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|a^2=e,b^2=d,b^a=bc,f^a=f^2,g^a=f^2g,h^a=h^4,f^b=f^2g^2,f^c=f^2,g^c=g^2108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1907);