Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D5×S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| derived | C5×A4 ⋊ C4×C8 |
| Sylow | C5 ⋊ C8×SL(2,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C4 | D5×S4 |
| commutator, hypocenter | C5×A4 | C4×C8 |
| Fitting | C23×C4×C5 | C2×D3 |
| socle | C24×C5 | C4×D3 |
| prime radical | C22×C5×A4 | C2×C4 |
| cosocle | C2×C4×C5×A4 | C22 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C2×C4 | |
374 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^5,3,5,2^2|a^2=d,b^2=c,c^2=e,d^2=e,g^a=g^4,f^b=f^2,h^b=hi,h^f=i,i^f=hi160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237464);