Finite Group DatabasebetaFinite Group Databasebeta| order | 9916 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×Dic67 |
| unambiguous semidirect product | C67⋊(C4×C37) |
| derived, Sylow | C67 ⋊ C4×C37 |
| Hall | C37×C67 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | D67 |
| commutator, hypocenter | C67 | C4×C37 |
| Frattini | C2 | C37×D67 |
| Fitting, socle, prime radical | C2×C37×C67 | C2 |
| cosocle | C2×C67 | C2×C37 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C2×C37 | |
12 conjugacy classes of subgroups.
2590 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C37×Dic67, C37×Dic201, C37×(C67⋊C3)⋊C4, … |
| maximal normal subgroup of | C3×C37×Dic67, C37×(C67⋊C3)⋊C4, C37⋊C3×Dic67, … |
| maximal quotient of | C3×C37×Dic67, C37×Dic201 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9916, 3);