Finite Group DatabasebetaFinite Group Databasebeta| order | 8961 |
| isoclinism | isoclinic class of C103⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×C103⋊C3 |
| unambiguous semidirect product | C103⋊(C3×C29) |
| unambiguous semidirect product | (C29×C103)⋊C3 |
| Fitting, socle, Hall | C29×C103 ⋊ C3 |
| derived, Sylow | C103 ⋊ C3×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | C103⋊C3 |
| commutator, hypocenter | C103 | C3×C29 |
| Frattini | C1 | G |
| Fitting, socle | C29×C103 | C3 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C29 | |
8 conjugacy classes of subgroups.
1073 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C29×C103⋊C3, C29×D103⋊C3, D29×C103⋊C3, … |
| maximal normal subgroup of | C2×C29×C103⋊C3, C29×D103⋊C3, D29×C103⋊C3, … |
| maximal quotient of | C2×C29×C103⋊C3, C29×C103⋊C9, C3×C29×C103⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8961, 1);