Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Hall | C32×C5 ⋊ #95 |
| Sylow | C32 ⋊ (C2×AGL(1,𝔽5))⋊C4 |
| Sylow | C5 ⋊ #63781 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D5⋊#157 |
| commutator | C2×C32×C5 | C42 |
| Fitting, socle | C22×C32×C5 | C2×C4 |
| prime radical, cosocle | C22×C3⋊D15 | C22 |
| hypocenter | C32×C5 | #95 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
260 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 43 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=c,b^2=d,b^a=be,f^a=fg,g^a=fg^2,h^a=h^2,f^b=f^2,g^b=g^2,f^c=f^2,g^c=g^2,h^c=h^460 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1860);