Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C210 |
| direct product | C24×C5×D5 |
| unambiguous semidirect product | C5⋊(C25×C5) |
| unambiguous semidirect product | (C2×C5)⋊(C24×C5) |
| Fitting, socle | C24×C52 ⋊ C2 |
| derived | C5 ⋊ C25×C5 |
| Sylow | C52 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C5 | D5 |
| commutator, cosocle, hypocenter | C5 | C25×C5 |
| Frattini | C1 | G |
| Fitting, socle | C24×C52 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C24×C5 | |
1630 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13101882, C5×#65244, C5×#65800, … |
| maximal normal subgroup of | #13101882, C5×#65244, C5×#65800, … |
| maximal quotient of | C23×C5×Dic10, C23×C4×C5×D5, C23×C5×D20, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1209);