Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×C4⋊#87604 |
| unambiguous semidirect product | D97⋊(C2×C4⋊C4) |
| Fitting | C22×C4×C97 ⋊ C4 |
| Sylow | C97 ⋊ C22×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×#87604 |
| commutator | C2×C97 | C23×C4 |
| Frattini | C2 | C23×#87604 |
| Fitting | C22×C4×C97 | C4 |
| socle | C23×C97 | C2×C4 |
| hypercenter | C22×C4 | #87604 |
| hypocenter | C97 | C22×C4⋊C4 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
418 conjugacy classes of subgroups.
424 conjugacy classes — view the full character table.
| maximal subgroup of | #27156913, #27156914, #27156916, … |
| maximal normal subgroup of | #27156913, #27156914, #27156916, … |
| maximal quotient of | C22×(C2×#87604)⋊C4, C2×C4×C4⋊#87604, C2×#20261677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1611);