Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C4×#13095486 |
| derived, Sylow | C97 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D97 |
| commutator, hypocenter | C97 | C4×C16 |
| Frattini | C2×C8 | C2×D97 |
| Fitting | C4×C8×C97 | C2 |
| socle | C22×C97 | C2×C8 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C4×C8 | |
58 conjugacy classes of subgroups.
1600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×#11715895, C8×#13095486, #27139652, … |
| maximal normal subgroup of | C16×#11715895, C8×#13095486, #27139652, … |
| maximal quotient of | C8×#13095486, #27139654, #27139814, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 323);