Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#15690840 |
| Sylow | C97 ⋊ C2×#137 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×C22⋊D97 |
| commutator | C4×C97 | C24 |
| Frattini | C4 | C23×D97 |
| Fitting | C2×#41×C97 | C2 |
| socle | C22×C97 | C2×D4 |
| hypercenter | C2×#41 | D97 |
| hypocenter | C97 | C2×#137 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C2×#41 | |
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
982 conjugacy classes — view the full character table.
| maximal subgroup of | #27142103, #27142105, #27142207, … |
| maximal normal subgroup of | #27142103, #27142105, #27142207, … |
| maximal quotient of | C2×#20260743, C2×#20260736, C2×#20260778, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1341);