Finite Group DatabasebetaFinite Group Databasebeta| order | 980 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×Dic7 |
| unambiguous semidirect product | C7⋊(C4×C5×C7) |
| derived | C7 ⋊ C4×C5×C7 |
| Hall | C5×C72 ⋊ C4 |
| Sylow | C72 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C7 | D7 |
| commutator, hypocenter | C7 | C4×C5×C7 |
| Frattini | C2 | C5×C7×D7 |
| Fitting, socle, prime radical | C2×C5×C72 | C2 |
| cosocle | C2×C7 | C2×C5×C7 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C5×C7 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 140 |
350 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D7×Dic7, C5×#87639, C5×#87641, … |
| maximal normal subgroup of | C5×D7×Dic7, C5×#87639, C5×#87641, … |
| maximal quotient of | C5×C7×C7⋊C8, C2×C5×C7×Dic7, C3×C5×C7×Dic7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(980, 12);