Finite Group DatabasebetaFinite Group Databasebeta| order | 6304 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C197 · Schur multiplier (H2) = C22 |
| direct product | #99×C197 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C197 | C22⋊C4 |
| commutator | C22 | C2×C4×C197 |
| Frattini, cosocle | C23 | C22×C197 |
| prime radical | C2×D4×C197 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C197 ◁ C23×C197 ◁ G | |
52 conjugacy classes of subgroups.
2167 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AΣL(1,𝔽16)×C197, #352×C197, #353×C197, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×C197, #352×C197, #353×C197, … |
| maximal quotient of | #323×C197, #324×C197, #327×C197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6304, 6);