Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C97 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×C22⋊C4×C97 |
| unambiguous semidirect product | C22⋊(C42×C97) |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C97 | C22 |
| commutator | C2 | C2×C42×C97 |
| Frattini, cosocle | C23 | C23×C97 |
| socle | C23×C97 | C23 |
| prime radical | C24×C97 | C22 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C97 ◁ G | |
258 conjugacy classes of subgroups.
3880 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C97×#1282, C97×#1284, C97×#1297, … |
| maximal normal subgroup of | C97×#1282, C97×#1284, C97×#1297, … |
| maximal quotient of | C4×#95×C97, C97×C22⋊#95, C97×#1434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 58);