Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of Dic50 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×C22⋊D25 |
| Fitting | C25×C25 ⋊ C2 |
| Sylow | C25 ⋊ C23×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D25 |
| commutator, cosocle | C2×C25 | C25 |
| Frattini | C2×C5 | C24×D5 |
| Fitting | C25×C25 | C2 |
| socle | C24×C5 | C2×D5 |
| hypercenter | C25 | D25 |
| hypocenter | C25 | C23×D4 |
| LCS | G ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C24 ◁ C25 | |
2043 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
424 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2053);