Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C5 |
No aliases for this group.
| Fitting | C42×C52 ⋊ C4 |
| Sylow | C52 ⋊ #383 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#1044 |
| commutator, socle | C22×C52 | C22×C4 |
| Fitting | C42×C52 | C4 |
| prime radical, cosocle | C22×C5⋊D5 | C23 |
| hypercenter | C42 | #1044 |
| hypocenter | C52 | #383 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C42 | |
384 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^6,5^2|a^2=d,b^2=e,c^2=f,b^a=bf,c^a=cef,g^a=g^3,h^a=h^2,g^d=g^4,h^d=h^4124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7180);