Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C4×#13182032 |
| derived, Sylow | C109 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #89137 |
| commutator, hypocenter | C109 | C4×C16 |
| Frattini | C2×C4 | C2×#89137 |
| Fitting | C42×C109 | C4 |
| socle | C22×C109 | C2×C8 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C42 | |
58 conjugacy classes of subgroups.
496 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#13182032, #28377944, #28377945, … |
| maximal normal subgroup of | C8×#13182032, #28377944, #28377945, … |
| maximal quotient of | C8×#13182032, #28377945, #28378070, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1434);