Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C5 |
| direct product | Q8×#6045 |
| Sylow | C52 ⋊ Q82 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×C5⋊D5 |
| commutator, socle, prime radical, cosocle | C22×C52 | C24 |
| Fitting | C4×C52×Q8 | C2 |
| hypercenter | C4×Q8 | C5⋊D5 |
| hypocenter | C52 | Q82 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
848 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1600 |
265 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9446);