Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×Dic25 |
| derived | C25 ⋊ C2×C4×C5 |
| Sylow | C5×C25 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | D25 |
| commutator, hypocenter | C25 | C2×C4×C5 |
| Frattini | C2×C5 | C2×C5×D5 |
| Fitting | C22×C5×C25 | C2 |
| socle, prime radical | C22×C52 | D5 |
| cosocle | C2×C25 | C22×C5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C22×C5 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic5×Dic25, #14522140, #14522141, … |
| maximal normal subgroup of | Dic5×Dic25, #14522140, #14522141, … |
| maximal quotient of | C2×C5×#6014, C5×#87716, C4×C5×Dic25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 59);