Finite Group DatabasebetaFinite Group Databasebeta| order | 8470 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C112 · Schur multiplier (H2) = C11 |
| direct product | C5×C112×D7 |
| unambiguous semidirect product | C7⋊(C2×C5×C112) |
| Fitting, socle, Hall | C5×C7×C112 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C5×C112 |
| Hall | C7×C112 ⋊ C2×C5 |
| Hall | C5×C7 ⋊ C2×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C112 | D7 |
| commutator, hypocenter | C7 | C2×C5×C112 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C112 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C5×C112 | |
112 conjugacy classes of subgroups.
3025 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C11×D7×D11, C5×D7×C11⋊D11, D5×C112×D7, … |
| maximal normal subgroup of | C5×C11×D7×D11, C5×D7×C11⋊D11, D5×C112×D7, … |
| maximal quotient of | C5×C112×Dic7, C2×C5×C112×D7, C3×C5×C112×D7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8470, 46);