Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C25×C5 ⋊ C2×D3 |
| Sylow | C5 ⋊ #85493 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D5×S4 |
| commutator, cosocle | C22×C5×A4 | C23 |
| Fitting | C25×C5 | C2×D3 |
| socle | C24×C5 | C22×D3 |
| hypercenter | C23 | D5×S4 |
| hypocenter | C5×A4 | #120 |
| LCS | G ▷ C22×C5×A4 ▷ C5×A4 | |
| UCS | C1 ◁ C22 ◁ C23 | |
1406 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 1406 conjugacy classes of subgroups — too many to draw. Only its 71 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:
2^5,3,5,2^2|c^a=ce,g^a=g^4,c^b=cd,f^b=f^2,h^b=hi,h^f=i,i^f=hi94 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239371);