Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #73048 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×#857 |
| commutator, cosocle | C2×C5×C42⋊C3 | C22 |
| Frattini | C23 | D5×S4 |
| Fitting | C2×C42×C5 | C2×D3 |
| socle | C23×C5 | C2×S4 |
| hypocenter | C5×C42⋊C3 | D4 |
| LCS | G ▷ C2×C5×C42⋊C3 ▷ C5×C42⋊C3 | |
| UCS | C1 ◁ C2 | |
334 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 24 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:
2^3,3,5,2^4|f^2=h,g^2=i,b^a=bc,e^a=e^4,d^b=d^2,f^b=fgi,g^b=gi,h^b=hi,f^d=gh,g^d=fg,h^d=i,i^d=hi68 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237332);