Finite Group DatabasebetaFinite Group Databasebeta| order | 980 |
| isoclinism | isoclinic class of D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic49 |
| unambiguous semidirect product | C49⋊(C4×C5) |
| derived, Sylow | C49 ⋊ C4×C5 |
| Hall | C5×C49 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D49 |
| commutator, hypocenter | C49 | C4×C5 |
| Frattini | C2×C7 | C5×D7 |
| Fitting | C2×C5×C49 | C2 |
| socle, prime radical | C2×C5×C7 | D7 |
| cosocle | C2×C49 | C2×C5 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C2×C5 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 980 |
260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14519910, #14519912, D5×Dic49, … |
| maximal normal subgroup of | #14519910, #14519912, D5×Dic49, … |
| maximal quotient of | C5×C49⋊C8, C2×C5×Dic49, C3×C5×Dic49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(980, 2);