Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C5 |
| direct product | C2×#11717520 |
| Fitting | C22×C52×Q8 ⋊ C2 |
| Sylow | C52 ⋊ C2×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×C5⋊D5 |
| commutator, cosocle | C2×C52 | C25 |
| Frattini | C2 | C24×C5⋊D5 |
| Fitting | C22×C52×Q8 | C2 |
| socle | C22×C52 | C24 |
| hypercenter | C22×Q8 | C5⋊D5 |
| hypocenter | C52 | C2×2−1+4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
3176 conjugacy classes of subgroups; only the 867 normal subgroups are shown.
This group has 3176 conjugacy classes of subgroups — too many to draw. Only its 867 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 800 |
274 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10236);