Finite Group DatabasebetaFinite Group Databasebeta| order | 980 |
| isoclinism | isoclinic class of #5997 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C7 |
| direct product | C5×#5997 |
| Fitting, socle, Hall | C5×C72 ⋊ C4 |
| derived, Sylow | C72 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #5997 |
| commutator, hypocenter | C72 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72 | C4 |
| prime radical | C5×C7⋊D7 | C2 |
| cosocle | C7⋊D7 | C2×C5 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C5 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 70 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#87656, #14520017, D5×#5997, … |
| maximal normal subgroup of | C5×#87656, #14520017, D5×#5997, … |
| maximal quotient of | C5×#87637, C2×C5×#5997, C3×C5×#5997, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(980, 18);