Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×C5×#41 ⋊ C2×C3 |
| Hall | C22×#4150 ⋊ C3 |
| Sylow | C5 ⋊ #87545 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D5×C22⋊A4 |
| commutator, cosocle, hypocenter | C22×C5×Q8 | C22×C3 |
| Fitting | C22×C5×#41 | C2×C3 |
| socle | C23×C5 | C22×A4 |
| hypercenter | C4 | D5×C22⋊A4 |
| LCS | G ▷ C22×C5×Q8 | |
| UCS | C1 ◁ C2 ◁ C4 | |
2094 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 2094 conjugacy classes of subgroups — too many to draw. Only its 60 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:
2^2,3,2^4,5,2|b^2=i,f^2=i,g^2=i,b^a=bi,h^a=h^4,d^c=de,e^c=d,f^c=fg,g^c=f,g^f=gi84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240380);