Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Hall | C3×C5 ⋊ #2388 |
| Sylow | C5 ⋊ #76777 |
| Sylow | C3 ⋊ #10608900 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D3×D5 |
| commutator, socle, cosocle | C23×C3×C5 | C24 |
| Fitting | C22×C3×C5×Q8 | C22 |
| hypercenter | C22×Q8 | D3×D5 |
| hypocenter | C3×C5 | #2388 |
| LCS | G ▷ C23×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
1888 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1888 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|d^2=e,b^a=be,c^a=cf,h^a=h^2,i^a=i^4,c^b=cg,h^b=h^2,i^b=i^4,i^c=i^4,h^d=h^2,i^d=i^4150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 57364);