Finite Group DatabasebetaFinite Group Databasebeta| order | 8470 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C112 · Schur multiplier (H2) = C11 |
| direct product | C7×D5×C112 |
| unambiguous semidirect product | C5⋊(C2×C7×C112) |
| Fitting, socle, Hall | C5×C7×C112 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C7×C112 |
| Hall | C5×C112 ⋊ C2×C7 |
| Hall | C5×C7 ⋊ C2×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C112 | D5 |
| commutator, hypocenter | C5 | C2×C7×C112 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C112 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C7×C112 | |
112 conjugacy classes of subgroups.
3388 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8470, 49);