Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#11719908 |
| derived, Sylow | C53 ⋊ C2×C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C8 | D53 |
| commutator, hypocenter | C53 | C2×C4×C16 |
| Frattini | C2×C8 | C22×D53 |
| Fitting | C2×C4×C8×C53 | C2 |
| socle | C23×C53 | C2×C8 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C4×C8 | |
216 conjugacy classes of subgroups.
1792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27270919, #27270920, #27270931, … |
| maximal normal subgroup of | #27270919, #27270920, #27270931, … |
| maximal quotient of | C2×C8×#11719908, C2×#20272633, M16×#11719908, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6097);