Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#11715906 |
| unambiguous semidirect product | #87604⋊(C2×C8) |
| Fitting | C2×C4×C97 ⋊ C8 |
| derived, Sylow | C97 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11715906 |
| commutator, hypocenter | C97 | C2×C4×C8 |
| Frattini | C2 | C22×#11715906 |
| Fitting | C2×C4×C97 | C8 |
| socle | C22×C97 | C2×C8 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C2×C4 | |
162 conjugacy classes of subgroups.
160 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#11715906)⋊C8, #27158743, #27158744, … |
| maximal normal subgroup of | (C2×#11715906)⋊C8, #27158743, #27158744, … |
| maximal quotient of | C2×C8×#11715906, C2×#20261819, M16×#11715906, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1659);