Finite Group DatabasebetaFinite Group Databasebeta| order | 6224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q8×D389 |
| Fitting | Q8×C389 ⋊ C2 |
| Sylow | C389 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D389 |
| commutator, socle | C2×C389 | C23 |
| Fitting | Q8×C389 | C2 |
| hypercenter | Q8 | D389 |
| hypocenter | C389 | C2×Q8 |
| LCS | G ▷ C2×C389 ▷ C389 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
38 conjugacy classes of subgroups.
980 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×D389, Q16×D389, #27159413, … |
| maximal normal subgroup of | SD16×D389, Q16×D389, #27159413, … |
| maximal quotient of | C4⋊C4×D389, #27159349, Q8×Dic389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6224, 37);