Finite Group DatabasebetaFinite Group Databasebeta| order | 6704 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C419 · Schur multiplier (H2) = C2 |
| direct product | D8×C419 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C419 | D4 |
| commutator, Frattini, cosocle | C4 | C22×C419 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C419 ◁ C4×C419 ◁ G | |
22 conjugacy classes of subgroups.
2933 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D16×C419, SD32×C419, C2×D8×C419, … |
| maximal normal subgroup of | D16×C419, SD32×C419, C2×D8×C419, … |
| maximal quotient of | #102×C419, #107×C419, D16×C419, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6704, 7);