Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
| direct product | C2×#16812753 |
| Fitting | C2×C8×C109 ⋊ C4 |
| Sylow | C109 ⋊ C2×#97 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×#89137 |
| commutator | C2×C109 | C2×C42 |
| Frattini | C4 | C22×#89137 |
| Fitting | C2×C8×C109 | C4 |
| socle | C22×C109 | C42 |
| hypercenter | C2×C8 | #89137 |
| hypocenter | C109 | C2×#97 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C8 | |
146 conjugacy classes of subgroups.
472 conjugacy classes — view the full character table.
| maximal subgroup of | #28378072, #28378078, #97×#89137, … |
| maximal normal subgroup of | #28378072, #28378078, #97×#89137, … |
| maximal quotient of | C2×#20295867, #28378226, C2×#11724786⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1506);