Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C5 |
No aliases for this group.
| Fitting | C52×M32 ⋊ C2 |
| Sylow | C52 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×C5⋊D5 |
| commutator, socle | C2×C52 | C22×C8 |
| Fitting | C52×M32 | C2 |
| prime radical | #87900 | C4 |
| cosocle | C52×C8 | C23 |
| hypercenter | M32 | C5⋊D5 |
| hypocenter | C52 | #504 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C8 ◁ M32 | |
336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^6,5^2|c^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^4,h^a=h^4,c^b=cf280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5122);