Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×C5×#392 ⋊ C2 |
| Hall | C3×C5 ⋊ #2388 |
| Sylow | C5 ⋊ #76665 |
| Sylow | C3 ⋊ #10608396 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D15 |
| commutator, socle, cosocle | C23×C3×C5 | C24 |
| Fitting | C3×C5×#392 | C2 |
| hypercenter | #392 | D15 |
| hypocenter | C3×C5 | #2388 |
| LCS | G ▷ C23×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C23 ◁ #392 | |
1888 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|d^2=e,b^a=be,c^a=cf,c^b=cg,h^d=h^2,i^d=i^4198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 57304);