Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C29 |
| direct product | C5×D5×2−1+4 |
| Fitting | C52×2−1+4 ⋊ C2 |
| Sylow | C52 ⋊ C2×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C5 | C24×D5 |
| commutator, cosocle | C2×C5 | C25×C5 |
| Frattini | C2 | C24×C5×D5 |
| Fitting | C52×2−1+4 | C2 |
| socle | C2×C52 | C25 |
| hypercenter | C5×2−1+4 | D5 |
| hypocenter | C5 | C2×C5×2−1+4 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C5 ◁ C5×2−1+4 | |
1734 conjugacy classes of subgroups; only the 890 normal subgroups are shown.
This group has 1734 conjugacy classes of subgroups — too many to draw. Only its 890 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10223);