Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×#11724786 |
| derived, Sylow | C109 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #89137 |
| commutator, hypocenter | C109 | C82 |
| Frattini | C2×C4 | C2×#89137 |
| Fitting | C2×C8×C109 | C4 |
| socle | C22×C109 | C42 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C2×C8 | |
74 conjugacy classes of subgroups.
496 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#11724786, #28377943, #11724786⋊C16, … |
| maximal normal subgroup of | C16×#11724786, #28377943, #11724786⋊C16, … |
| maximal quotient of | #28377854, C16×#11724786, C8×#13182032, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1389);