Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#384 ⋊ D3 |
| Sylow | C5 ⋊ #72994 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11752116 |
| commutator, cosocle | C2×C5×C42⋊C3 | C22 |
| Frattini | C23 | C2×C5⋊S4 |
| Fitting | C5×#384 | D3 |
| socle | C23×C5 | C2×S4 |
| hypocenter | C5×C42⋊C3 | D4 |
| LCS | G ▷ C2×C5×C42⋊C3 ▷ C5×C42⋊C3 | |
| UCS | C1 ◁ C2 | |
298 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 25 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|b^2=c,f^2=h,g^2=i,b^a=bc,d^a=d^2,e^a=e^4,f^a=fg,g^a=gi,h^a=hi,f^b=fh,g^b=gi,f^d=ghi,g^d=fgh,h^d=i,i^d=hi62 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237606);