Finite Group DatabasebetaFinite Group Databasebeta| order | 8330 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7×C17 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×D7×C17 |
| unambiguous semidirect product | C7⋊(C2×C5×C7×C17) |
| Fitting, socle, Hall | C5×C72×C17 ⋊ C2 |
| derived | C7 ⋊ C2×C5×C7×C17 |
| Hall | C72×C17 ⋊ C2×C5 |
| Hall | C5×C72 ⋊ C2×C17 |
| Sylow | C72 ⋊ C2×C5×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7×C17 | D7 |
| commutator, hypocenter | C7 | C2×C5×C7×C17 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C17 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C5×C7×C17 | |
44 conjugacy classes of subgroups.
2975 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C7×D7×D17, C5×D72×C17, C5×D7×D119, … |
| maximal normal subgroup of | C5×C7×D7×D17, C5×D72×C17, C5×D7×D119, … |
| maximal quotient of | C5×C7×C17×Dic7, C2×C5×C7×D7×C17, C3×C5×C7×D7×C17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8330, 11);