Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q16×#89137 |
| Fitting | Q16×C109 ⋊ C4 |
| Sylow | C109 ⋊ C4×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×#89137 |
| commutator | C4×C109 | C22×C4 |
| Frattini | C4 | C22×#89137 |
| Fitting | Q16×C109 | C4 |
| socle | C2×C109 | C4×D4 |
| hypercenter | Q16 | #89137 |
| hypocenter | C109 | C4×Q16 |
| LCS | G ▷ C4×C109 ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
110 conjugacy classes of subgroups.
217 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×#89137, Q32×#89137, #28379428, … |
| maximal normal subgroup of | SD32×#89137, Q32×#89137, #28379428, … |
| maximal quotient of | Q16×#11724786, #28378619, #28378620, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1587);