Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D16×D97 |
| Fitting | D16×C97 ⋊ C2 |
| Sylow | C97 ⋊ C2×D16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D8×D97 |
| commutator | C8×C97 | C23 |
| Frattini | C8 | C22×D97 |
| Fitting | D16×C97 | C2 |
| socle | C2×C97 | C2×D8 |
| hypercenter | D16 | D97 |
| hypocenter | C97 | C2×D16 |
| LCS | G ▷ C8×C97 ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ D16 | |
98 conjugacy classes of subgroups.
550 conjugacy classes — view the full character table.
| maximal subgroup of | D32×D97, SD64×D97, #27144047, … |
| maximal normal subgroup of | D32×D97, SD64×D97, #27144047, … |
| maximal quotient of | #357×D97, #366×D97, #27143580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 968);