Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×C5×Q8 ⋊ C2×D3 |
| Sylow | C5 ⋊ #87489 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D5×S4 |
| commutator, cosocle | C2×C5×A4 | C24 |
| Fitting | C22×C5×Q8 | C2×D3 |
| socle | C23×C5 | C23×D3 |
| hypercenter | Q8 | D5×S4 |
| hypocenter | C5×A4 | H(5,𝔽2) |
| LCS | G ▷ C2×C5×A4 ▷ C5×A4 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
1720 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^5,3,5,2^2|c^2=e,d^2=e,d^a=de,g^a=g^4,c^b=ce,f^b=f^2,h^b=hi,d^c=de,h^f=i,i^f=hi94 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240180);