Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×C22⋊#87604 |
| Fitting | C22×C4×C97 ⋊ C4 |
| Sylow | C97 ⋊ C4×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×#87604 |
| commutator | C2×C97 | C2×C42 |
| Frattini | C22 | C22×#87604 |
| Fitting | C22×C4×C97 | C4 |
| socle | C22×C97 | C22×C4 |
| hypercenter | C22×C4 | #87604 |
| hypocenter | C97 | C4×C22⋊C4 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
258 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
424 conjugacy classes — view the full character table.
| maximal subgroup of | #27156577, #27156578, #27156583, … |
| maximal normal subgroup of | #27156577, #27156578, #27156583, … |
| maximal quotient of | C4×(C2×#87604)⋊C4, #27156910, #27156912, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1486);