Finite Group DatabasebetaFinite Group Databasebeta| order | 6224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×D389 |
| unambiguous semidirect product | C389⋊C24 |
| unambiguous semidirect product | (C2×C389)⋊C23 |
| Fitting, socle | C23×C389 ⋊ C2 |
| derived, Sylow | C389 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D389 |
| commutator, hypocenter | C389 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C23×C389 | C2 |
| LCS | G ▷ C389 | |
| UCS | C1 ◁ C23 | |
134 conjugacy classes of subgroups.
1568 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×D389, C2×#20261943, #27159352, … |
| maximal normal subgroup of | C22⋊C4×D389, C2×#20261943, #27159352, … |
| maximal quotient of | C22×C4×D389, C23×Dic389, C2×D4×D389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6224, 42);