Finite Group DatabasebetaFinite Group Databasebeta| order | 6704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C419 ⋊ SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D419 |
| commutator | C4×C419 | C22 |
| Frattini | C4 | C2×D419 |
| Fitting | D4×C419 | C2 |
| socle | C2×C419 | D4 |
| hypercenter | D4 | D419 |
| hypocenter | C419 | SD16 |
| LCS | G ▷ C4×C419 ▷ C2×C419 ▷ C419 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,419|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^418,c^b=cd1052 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16×D419, C2×#20269399, #27211737, … |
| maximal normal subgroup of | SD16×D419, C2×#20269399, #27211737, … |
| maximal quotient of | #27211639, #27211641, #27211649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6704, 28);