Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C23×C5×D4 ⋊ D3 |
| Sylow | C5 ⋊ #87477 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×C5⋊S4 |
| commutator, cosocle | C2×C5×A4 | C24 |
| Fitting | C23×C5×D4 | D3 |
| socle | C23×C5 | C23×D3 |
| hypercenter | C2×D4 | C5⋊S4 |
| hypocenter | C5×A4 | H(5,𝔽2) |
| LCS | G ▷ C2×C5×A4 ▷ C5×A4 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
1814 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 1814 conjugacy classes of subgroups — too many to draw. Only its 153 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|d^a=de,f^a=f^2,g^a=g^4,h^a=hi,c^b=ce,h^f=i,i^f=hi124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240293);