Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#11724786 |
| Sylow | C109 ⋊ C2×C22⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×#89137 |
| commutator | C2×C109 | C22×C8 |
| Frattini | C22 | C22×#89137 |
| Fitting | C24×C109 | C4 |
| socle | C23×C109 | C2×C4 |
| hypercenter | C24 | #89137 |
| hypocenter | C109 | C2×C22⋊C8 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C23 ◁ C24 | |
202 conjugacy classes of subgroups.
472 conjugacy classes — view the full character table.
| maximal subgroup of | #28377870, #28377875, C2×#20295869, … |
| maximal normal subgroup of | #28377870, #28377875, C2×#20295869, … |
| maximal quotient of | C2×#20295869, C2×#20295871, #28378263, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1516);