Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #10600209⋊C3 |
| derived | C5×#95 ⋊ C3×C4 |
| Hall | #10600209 ⋊ C3 |
| Sylow | C5 ⋊ #1443⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C5⋊(#126⋊C3) |
| commutator, hypocenter | C5×#95 | C3×C4 |
| Frattini | C24 | D5×A4 |
| Fitting, cosocle | C2×C5×#95 | C2×C3 |
| socle | C24×C5 | C2×A4 |
| prime radical | C2×C5×#95⋊C3 | C2 |
| LCS | G ▷ C5×#95 | |
| UCS | C1 ◁ C22 | |
222 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2,3,2^3,5,2^3|a^2=c,d^2=g,e^2=ghi,d^a=dhi,e^a=eh,f^a=f^4,d^b=de,e^b=di,g^b=gi,h^b=hi,i^b=h,e^d=egh84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237256);