Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D109⋊M32 |
| Sylow | C109 ⋊ C2×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C2×#89137 |
| commutator, socle | C2×C109 | C22×C8 |
| Frattini | C4 | C22×#89137 |
| Fitting | C2×C8×C109 | C4 |
| hypercenter | C2×C8 | #89137 |
| hypocenter | C109 | C2×M32 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C8 ◁ C2×C8 | |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^33,g^c=g^108,g^d=g^108472 conjugacy classes — view the full character table.
| maximal subgroup of | #28378075, #28378078, #28378081, … |
| maximal normal subgroup of | #28378075, #28378078, #28378081, … |
| maximal quotient of | #28379233, #28379238, #28379239, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1605);