Finite Group DatabasebetaFinite Group Databasebeta| order | 9916 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C67⋊#3866 |
| Fitting, socle, derived, Hall | C37×C67 ⋊ C4 |
| Sylow | C67 ⋊ #3866 |
| Sylow | C37 ⋊ Dic67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C67 | C4 |
| prime radical, cosocle | C67×D37 | C2 |
| LCS | G ▷ C37×C67 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,37,67|a^2=b,c^a=c^31,d^a=d^66,c^b=c^36673 conjugacy classes — view the full character table.
| maximal subgroup of | #44446568, #44446569, #44446572, … |
| maximal normal subgroup of | #44446568, #44446569, #44446572, … |
| maximal quotient of | C3×C67⋊#3866, C3⋊(C67⋊#3866) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9916, 7);