Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #10619380 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×(C24⋊C5)⋊C2 |
| commutator, cosocle, hypocenter | C3×2−1+4⋊C5 | C22 |
| Fitting | C3×2−1+4 | C2×D5 |
| socle | C2×C3 | C2×(C24⋊C5)⋊C2 |
| LCS | G ▷ C3×2−1+4⋊C5 | |
| UCS | C1 ◁ C2 | |
412 conjugacy classes of subgroups; only the 15 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 15 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^2,3,5,2^5|e^2=i,f^2=i,g^2=i,b^a=bi,c^a=c^2,d^b=d^4,e^b=efghi,f^b=fh,g^b=ghi,e^d=f,f^d=fg,g^d=gh,h^d=ehi,f^e=fi,g^e=gi,h^e=hi,g^f=gi39 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240044);