Finite Group DatabasebetaFinite Group Databasebeta| order | 6704 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C419 · Schur multiplier (H2) = C1 |
| direct product | M16×C419 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C419 | C22 |
| commutator | C2 | C2×C4×C419 |
| Frattini, cosocle | C4 | C22×C419 |
| socle | C2×C419 | C2×C4 |
| prime radical | C22×C419 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C419 ◁ G | |
20 conjugacy classes of subgroups.
4190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #100×C419, #101×C419, #104×C419, … |
| maximal normal subgroup of | #100×C419, #101×C419, #104×C419, … |
| maximal quotient of | #97×C419, C22⋊C8×C419, C4⋊C8×C419, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6704, 6);