Finite Group DatabasebetaFinite Group Databasebeta| order | 6304 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C22⋊C4×D197 |
| Fitting | C22⋊C4×C197 ⋊ C2 |
| Sylow | C197 ⋊ C2×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D197 |
| commutator | C2×C197 | C22×C4 |
| Fitting | C22⋊C4×C197 | C2 |
| socle | C22×C197 | C23 |
| hypercenter | C22⋊C4 | D197 |
| hypocenter | C197 | C2×C22⋊C4 |
| LCS | G ▷ C2×C197 ▷ C197 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
132 conjugacy classes of subgroups.
1000 conjugacy classes — view the full character table.
| maximal subgroup of | #99×D197, C2×C22⋊C4×D197, #117×D197, … |
| maximal normal subgroup of | #99×D197, C2×C22⋊C4×D197, #117×D197, … |
| maximal quotient of | #95×D197, #27160926, C22⋊C4×Dic197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6304, 96);