Finite Group DatabasebetaFinite Group Databasebeta| order | 6304 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#13096802 |
| derived, Sylow | C197 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D197 |
| commutator, hypocenter | C197 | C4×C8 |
| Frattini | C2×C4 | C2×D197 |
| Fitting | C42×C197 | C2 |
| socle | C22×C197 | C2×C4 |
| LCS | G ▷ C197 | |
| UCS | C1 ◁ C42 | |
44 conjugacy classes of subgroups.
1600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#13096802, #27160800, #27160801, … |
| maximal normal subgroup of | C8×#13096802, #27160800, #27160801, … |
| maximal quotient of | C8×#13096802, #27160800, #27160834, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6304, 55);