Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C22×C42×C5 ⋊ D3 |
| Sylow | C5 ⋊ #85289 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×C5⋊S4 |
| commutator, cosocle | C22×C5×A4 | C23 |
| Fitting | C22×C42×C5 | D3 |
| socle | C24×C5 | C22×D3 |
| hypercenter | C42 | C5⋊S4 |
| hypocenter | C5×A4 | #127 |
| LCS | G ▷ C22×C5×A4 ▷ C5×A4 | |
| UCS | C1 ◁ C22 ◁ C42 | |
994 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 101 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:
2^5,3,5,2^2|b^2=e,c^2=d,b^a=be,c^a=cd,f^a=f^2,g^a=g^4,h^a=hi,h^f=i,i^f=hi172 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239389);