Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3×ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Hall | C32×C5 ⋊ C4×C8 |
| Sylow | C32 ⋊ C8×AGL(1,𝔽5) |
| Sylow | C5 ⋊ #63553 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×ΓL(1,𝔽16) |
| commutator, hypocenter | C32×C5 | C4×C8 |
| Fitting | C32×C4×C5 | C2×C4 |
| socle | C2×C32×C5 | C42 |
| prime radical | C2×C32×D5 | C2×C4 |
| cosocle | C32×C4×D5 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C4 | |
206 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 66 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|a^2=c,b^2=d,c^2=e,d^2=e,f^a=f^2,h^a=h^2,g^b=g^2,h^c=h^4108 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3710, #72229548, #72229562, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3710, #72229548, #72229562, … |
| maximal quotient of | #72231171, #72259968 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1760);