Finite Group DatabasebetaFinite Group Databasebeta| order | 6304 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×C22⋊D197 |
| Fitting | C22×C4×C197 ⋊ C2 |
| Sylow | C197 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D197 |
| commutator | C2×C197 | C22×C4 |
| Frattini | C22 | C22×D197 |
| Fitting | C22×C4×C197 | C2 |
| socle | C22×C197 | C23 |
| hypercenter | C22×C4 | D197 |
| hypocenter | C197 | C4×D4 |
| LCS | G ▷ C2×C197 ▷ C197 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
94 conjugacy classes of subgroups.
1588 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27161142, C8×C22⋊D197, #27161147, … |
| maximal normal subgroup of | #27161142, C8×C22⋊D197, #27161147, … |
| maximal quotient of | C4×C22⋊Dic197, C4×#15691335, C4×#15691337, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6304, 107);