Finite Group DatabasebetaFinite Group Databasebeta| order | 6304 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C197 · Schur multiplier (H2) = C1 |
| direct product | Q32×C197 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C2×C197 | D8 |
| commutator, Frattini, cosocle | C8 | C22×C197 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C197 ◁ C4×C197 ◁ C8×C197 ◁ G | |
24 conjugacy classes of subgroups.
2167 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD64×C197, Q64×C197, C2×Q32×C197, … |
| maximal normal subgroup of | SD64×C197, Q64×C197, C2×Q32×C197, … |
| maximal quotient of | #358×C197, #366×C197, C2×Q32×C197 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6304, 20);