Finite Group DatabasebetaFinite Group Databasebeta| order | 8241 |
| isoclinism | isoclinic class of C67⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×C67⋊C3 |
| unambiguous semidirect product | C67⋊(C3×C41) |
| unambiguous semidirect product | (C41×C67)⋊C3 |
| Fitting, socle, Hall | C41×C67 ⋊ C3 |
| derived, Sylow | C67 ⋊ C3×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | C67⋊C3 |
| commutator, hypocenter | C67 | C3×C41 |
| Frattini | C1 | G |
| Fitting, socle | C41×C67 | C3 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C41 | |
8 conjugacy classes of subgroups.
1025 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C41×C67⋊C3, C41×D67⋊C3, D41×C67⋊C3, … |
| maximal normal subgroup of | C2×C41×C67⋊C3, C41×D67⋊C3, D41×C67⋊C3, … |
| maximal quotient of | C2×C41×C67⋊C3, C41×C67⋊C9, C3×C41×C67⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8241, 1);