Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#13182032 |
| Sylow | C109 ⋊ C22⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×#89137 |
| commutator | C2×C109 | C2×C16 |
| Fitting | C22×C4×C109 | C4 |
| socle | C22×C109 | C2×C8 |
| hypercenter | C22×C4 | #89137 |
| hypocenter | C109 | C22⋊C16 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,d^2=e,e^2=f,b^a=bc,g^a=g^33,g^d=g^108472 conjugacy classes — view the full character table.
| maximal subgroup of | #28377952, #28377953, #28377954, … |
| maximal normal subgroup of | #28377952, #28377953, #28377954, … |
| maximal quotient of | #28377952, #28377968, D4⋊#13182032, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1443);