Finite Group DatabasebetaFinite Group Databasebeta| order | 8330 |
| isoclinism | isoclinic class of D85 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×D85 |
| unambiguous semidirect product | C5⋊(C72×D17) |
| unambiguous semidirect product | C17⋊(C72×D5) |
| Fitting, socle, Hall | C5×C72×C17 ⋊ C2 |
| derived, Hall | C5×C17 ⋊ C2×C72 |
| Hall | C72×C17 ⋊ D5 |
| Hall | C5×C72 ⋊ D17 |
| Sylow | C17 ⋊ C72×D5 |
| Sylow | C5 ⋊ C72×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D85 |
| commutator, hypocenter | C5×C17 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C17 | C2 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C72 | |
80 conjugacy classes of subgroups.
2156 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×#66775, C72×#66776, C7×C7⋊#66775, … |
| maximal normal subgroup of | C72×#66775, C72×#66776, C7×C7⋊#66775, … |
| maximal quotient of | C72×Dic85, C2×C72×D85, C3×C72×D85, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8330, 16);