Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #85566 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #11757174 |
| commutator, hypocenter | C5×#997 | C4 |
| Fitting | C5×H(5,𝔽2) | Dic3 |
| socle | C2×C5 | #5936 |
| prime radical, cosocle | C5⋊#5950 | C2 |
| LCS | G ▷ C5×#997 | |
| UCS | C1 ◁ C2 | |
332 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^2,3,5,2^5|a^2=b,b^2=i,c^a=c^2,d^a=d^2,e^a=ef,g^a=gh,d^b=d^4,e^c=f,f^c=ef,g^c=h,h^c=gh,h^e=hi,g^f=gi37 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240090);