Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C5×H(5,𝔽2) ⋊ D3 |
| Sylow | C5 ⋊ #87515 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×C5⋊#1020 |
| commutator, cosocle, hypocenter | C5×#997 | C22 |
| Fitting | C2×C5×H(5,𝔽2) | D3 |
| socle | C2×C5 | C2×#1020 |
| hypercenter | C22 | C5⋊#1020 |
| LCS | G ▷ C5×#997 | |
| UCS | C1 ◁ C2 ◁ C22 | |
596 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^2,3,5,2^5|b^a=bi,c^a=c^2,d^a=d^4,e^a=ef,g^a=gh,e^c=f,f^c=ef,g^c=h,h^c=gh,h^e=hi,g^f=gi67 conjugacy classes — view the full character table.
| maximal subgroup of | #72253873, D5×#87515 |
| maximal normal subgroup of | D5×#87515 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240331);