Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×#11715895 |
| derived, Sylow | C97 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D97 |
| commutator, hypocenter | C97 | C82 |
| Frattini | C42 | C2×D97 |
| Fitting | C4×C8×C97 | C2 |
| socle | C22×C97 | C42 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C4×C8 | |
74 conjugacy classes of subgroups.
1600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×#11715895, #27139652, #27139655, … |
| maximal normal subgroup of | C16×#11715895, #27139652, #27139655, … |
| maximal quotient of | #27139563, C16×#11715895, C8×#13095486, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 269);