Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#15690868 |
| Fitting | C24×C97 ⋊ C4 |
| Sylow | C97 ⋊ C2×#99 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊#87604 |
| commutator | C22×C97 | C22×C4 |
| Frattini | C22 | C22×#87604 |
| Fitting | C24×C97 | C4 |
| socle | C22×C97 | C22⋊C4 |
| hypercenter | C24 | #87604 |
| hypocenter | C97 | C2×#99 |
| LCS | G ▷ C22×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C23 ◁ C24 | |
210 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
406 conjugacy classes — view the full character table.
| maximal subgroup of | #27156820, #27156821, C4×#15690868, … |
| maximal normal subgroup of | #27156820, #27156821, C4×#15690868, … |
| maximal quotient of | C2×#20261578, C2×#20261581, #27156971, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1525);