Finite Group DatabasebetaFinite Group Databasebeta| order | 7736 |
| automorphism | Aut(G) order 7472976 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3868 |
| unambiguous semidirect product | C4⋊D967 |
| Fitting | C4×C967 ⋊ C2 |
| Sylow | C967 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D967 |
| commutator, socle | C2×C967 | C22 |
| Fitting | C4×C967 | C2 |
| hypercenter | C4 | D967 |
| hypocenter | C967 | D4 |
| LCS | G ▷ C2×C967 ▷ C967 | |
| UCS | C1 ◁ C2 ◁ C4 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,967|b^a=bc,d^a=d^966,d^b=d^9661937 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29509156, D7736, #29509158, … |
| maximal normal subgroup of | #29509156, D7736, #29509158, … |
| maximal quotient of | (C2×D967)⋊C4, C4⋊Dic967, D7736, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7736, 10);