Finite Group DatabasebetaFinite Group Databasebeta| order | 10234 |
| isoclinism | isoclinic class of D43 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C17 · Schur multiplier (H2) = C1 |
| direct product | C7×C17×D43 |
| Fitting, socle, Hall | C7×C17×C43 ⋊ C2 |
| derived, Sylow | C43 ⋊ C2×C7×C17 |
| Hall | C17×C43 ⋊ C2×C7 |
| Hall | C7×C43 ⋊ C2×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C17 | D43 |
| commutator, cosocle, hypocenter | C43 | C2×C7×C17 |
| Frattini | C1 | G |
| Fitting, socle | C7×C17×C43 | C2 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C7×C17 | |
16 conjugacy classes of subgroups.
2737 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D17×D43, D7×C17×D43, D43×D119, … |
| maximal normal subgroup of | C7×D17×D43, D7×C17×D43, D43×D119, … |
| maximal quotient of | C7×C17×Dic43, C2×C7×C17×D43, C3×C7×C17×D43, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10234, 3);