Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | #99×D97 |
| Fitting | #99×C97 ⋊ C2 |
| Sylow | C97 ⋊ C2×#99 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊C4×D97 |
| commutator | C22×C97 | C22×C4 |
| Frattini | C23 | C22×D97 |
| Fitting | #99×C97 | C2 |
| socle | C2×C97 | C2×C22⋊C4 |
| hypercenter | #99 | D97 |
| hypocenter | C97 | C2×#99 |
| LCS | G ▷ C22×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ #99 | |
210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
550 conjugacy classes — view the full character table.
| maximal subgroup of | AΣL(1,𝔽16)×D97, #352×D97, #27143379, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×D97, #352×D97, #27143379, … |
| maximal quotient of | #323×D97, #324×D97, #27140051, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 518);