Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#66165 |
| Fitting | C2×C52×#41 ⋊ C2 |
| Sylow | C52 ⋊ #548 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C5 | C23×D5 |
| commutator, cosocle | C22×C5 | C24×C5 |
| Frattini | C22 | C23×C5×D5 |
| Fitting | C2×C52×#41 | C2 |
| socle | C22×C52 | C24 |
| hypercenter | C2×C5×#41 | D5 |
| hypocenter | C5 | C5×#548 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C5 ◁ C2×C5×#41 | |
744 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 226 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
325 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9336);