Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #73038 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D5×S4 |
| commutator, hypocenter | C5×SL(2,𝔽3) | C2×C8 |
| Fitting | C5×#131 | C2×D3 |
| socle | C2×C5 | C8×S4 |
| prime radical | C5×#985 | C4 |
| cosocle | C5×#131⋊C3 | C22 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C8 | |
174 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 174 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) = 320 |
Polycyclic presentation:
2^4,3,5,2^3|a^2=c,c^2=d,d^2=i,g^2=i,h^2=i,f^a=f^4,e^b=e^2,g^b=gh,h^b=hi,g^e=h,h^e=ghi,h^g=hi128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237432);