Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ C4⋊((C24⋊C5)⋊C2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×(C24⋊C5)⋊C2 |
| commutator, cosocle | C2×C3×C24⋊C5 | C22 |
| Fitting, socle | C25×C3 | C2×D5 |
| hypocenter | C3×C24⋊C5 | D4 |
| LCS | G ▷ C2×C3×C24⋊C5 ▷ C3×C24⋊C5 | |
| UCS | C1 ◁ C2 | |
716 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 19 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|a^2=c,b^a=bc,d^a=d^2,e^b=e^4,f^b=fghi,g^b=gi,h^b=hi,f^e=g,g^e=gh,h^e=hi,i^e=fi48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240050);