Finite Group DatabasebetaFinite Group Databasebeta| order | 9916 |
| automorphism | Aut(G) order 11780208 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2479 |
| unambiguous semidirect product | C67⋊Dic37 |
| derived, Hall | C37×C67 ⋊ C4 |
| Sylow | C67 ⋊ Dic37 |
| Sylow | C37 ⋊ Dic67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2479 |
| commutator, hypocenter | C37×C67 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C37×C67 | C2 |
| LCS | G ▷ C37×C67 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,37,67,2|a^2=d,b^a=b^36,c^a=c^662482 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2479, Dic7437, (C67⋊C3)⋊Dic37, … |
| maximal normal subgroup of | C3×Dic2479, (C67⋊C3)⋊Dic37, #44446563, … |
| maximal quotient of | C3×Dic2479, Dic7437 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9916, 4);