Finite Group DatabasebetaFinite Group Databasebeta| order | 6304 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#15691333 |
| derived, Sylow | C197 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D197 |
| commutator, hypocenter | C197 | C2×C16 |
| Frattini | C8 | C2×D197 |
| Fitting | C2×C8×C197 | C2 |
| socle | C22×C197 | C8 |
| LCS | G ▷ C197 | |
| UCS | C1 ◁ C2×C8 | |
28 conjugacy classes of subgroups.
1600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×Dic197, C4×#15691333, #27160854, … |
| maximal normal subgroup of | C16×Dic197, C4×#15691333, #27160854, … |
| maximal quotient of | C4×#15691333, C22⋊#15691333, C4⋊#15691333, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6304, 84);