Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#16810380 |
| Sylow | C53 ⋊ C2×H(3,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic53 |
| commutator | C4×C53 | C2×C42 |
| Frattini | C22×C4 | C22×D53 |
| Fitting | C22×M16×C53 | C2 |
| socle | C22×C53 | #95 |
| hypercenter | C22×M16 | D53 |
| hypocenter | C53 | C2×H(3,ℤ/4) |
| LCS | G ▷ C4×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C22×M16 | |
404 conjugacy classes of subgroups.
1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271223, #27271225, #27271229, … |
| maximal normal subgroup of | #27271223, #27271225, #27271229, … |
| maximal quotient of | C2×#20272543, #27273490, #27273493, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4211);