Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C16 · Schur multiplier (H2) = C8 |
No aliases for this group.
| derived, Hall | C3×C5 ⋊ C8×C16 |
| Sylow | C5 ⋊ C16×C3⋊C8 |
| Sylow | C3 ⋊ C16×#170 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C8 | D3×AGL(1,𝔽5) |
| commutator, hypocenter | C3×C5 | C8×C16 |
| Fitting | C2×C3×C5×C8 | C2×C4 |
| socle, prime radical | C22×C3×C5 | C4×C8 |
| cosocle | C3×C8×Dic5 | C22 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C8 | |
208 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1920 |
Polycyclic presentation:
2^7,3,5|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,h^a=h^2,h^b=h^2,i^b=i^2,i^d=i^4240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 3146);