Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C3×C5×#564 ⋊ C2 |
| Hall | C3×C5 ⋊ #3531 |
| Sylow | C5 ⋊ #87139 |
| Sylow | C3 ⋊ #10619040 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C25 |
| Fitting | C3×C5×#564 | C2 |
| hypercenter | #564 | D15 |
| hypocenter | C3×C5 | #3531 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ #564 | |
1860 conjugacy classes of subgroups; only the 593 normal subgroups are shown.
This group has 1860 conjugacy classes of subgroups — too many to draw. Only its 593 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|b^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^a=dfg,h^a=h^2,i^a=i^4,c^b=cfg,d^b=df,h^d=h^2,i^d=i^4,h^e=h^2,i^e=i^4171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 221303);