Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| isoclinism | isoclinic class of #89137 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C16×#89137 |
| Fitting | C16×C109 ⋊ C4 |
| derived, Sylow | C109 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #89137 |
| commutator, hypocenter | C109 | C4×C16 |
| Frattini | C8 | C2×#89137 |
| Fitting | C16×C109 | C4 |
| socle | C2×C109 | C4×C8 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C16 | |
58 conjugacy classes of subgroups.
496 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#89137, #28378138, C2×C16×#89137, … |
| maximal normal subgroup of | C32×#89137, #28378138, C2×C16×#89137, … |
| maximal quotient of | C16×#11724786, #11724786⋊C16, (C2×#89137)⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1433);