Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of C5⋊#87588 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | C5⋊#87588 |
| Fitting, socle | C26×C5 ⋊ D3 |
| derived | C5×C22⋊(C22⋊A4) ⋊ C2 |
| Sylow | C5 ⋊ #87588 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×C22⋊(C22⋊A4) | C2 |
| Fitting, socle | C26×C5 | D3 |
| LCS | G ▷ C5×C22⋊(C22⋊A4) | |
| UCS | C1 | |
1660 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 1660 conjugacy classes of subgroups — too many to draw. Only its 35 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:
2,3,5,2^6|b^a=b^2,c^a=c^4,d^a=de,f^a=fg,h^a=hi,d^b=e,e^b=de,f^b=g,g^b=fg,h^b=i,i^b=hi72 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#87588 |
| maximal normal subgroup of | D5×#87588 |
| maximal quotient of | #72246151 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240413);