Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #104×D97 |
| Fitting | #104×C97 ⋊ C2 |
| Sylow | C97 ⋊ C2×#104 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | D4×D97 |
| commutator | C4×C97 | C22×C4 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | #104×C97 | C2 |
| socle | C2×C97 | C2×C22⋊C4 |
| hypercenter | #104 | D97 |
| hypocenter | C97 | C2×#104 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #104 | |
170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 170 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.
700 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#104×D97, #421×D97, #27150280, … |
| maximal normal subgroup of | C2×#104×D97, #421×D97, #27150280, … |
| maximal quotient of | D4⋊C8×D97, Q8⋊C8×D97, #27140115, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 560);