Finite Group DatabasebetaFinite Group Databasebeta| order | 6704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×Dic838 |
| unambiguous semidirect product | (C2×C419)⋊Q8 |
| Sylow | C419 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D419 |
| commutator | C2×C419 | C23 |
| Frattini | C2 | C22×D419 |
| Fitting | C2×C4×C419 | C2 |
| socle | C22×C419 | C22 |
| hypercenter | C2×C4 | D419 |
| hypocenter | C419 | C2×Q8 |
| LCS | G ▷ C2×C419 ▷ C419 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
38 conjugacy classes of subgroups.
1682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27211636, #27211641, #27211643, … |
| maximal normal subgroup of | #27211636, #27211641, #27211643, … |
| maximal quotient of | C2×Dic419⋊C4, C2×C4⋊Dic419, C4×Dic838, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6704, 38);