Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#41×D25 |
| Fitting | C2×#41×C25 ⋊ C2 |
| Sylow | C25 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D25 |
| commutator, cosocle | C2×C25 | C25 |
| Frattini | C2×C5 | C24×D5 |
| Fitting | C2×#41×C25 | C2 |
| socle | C22×C5 | C23×D5 |
| hypercenter | C2×#41 | D25 |
| hypocenter | C25 | C22×#41 |
| LCS | G ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
1335 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1335 conjugacy classes of subgroups — too many to draw. Only its 525 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2044);