Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #87524 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×#1020 |
| commutator, cosocle | C2×C5×C22⋊A4 | C22 |
| Fitting, socle | C25×C5 | C2×D3 |
| hypocenter | C5×C22⋊A4 | D4 |
| LCS | G ▷ C2×C5×C22⋊A4 ▷ C5×C22⋊A4 | |
| UCS | C1 ◁ C2 | |
1652 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 1652 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
Polycyclic presentation:
2^3,3,5,2^4|b^a=bc,e^a=e^4,d^b=d^2,f^b=fg,h^b=hi,f^d=g,g^d=fg,h^d=i,i^d=hi68 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#87524, #72243340, #72243416, … |
| maximal normal subgroup of | D5×#87524, #72243340, #72243416 |
| maximal quotient of | #72243498 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240263);