Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#13182004 |
| Sylow | C109 ⋊ C4⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C2×D109 |
| commutator | C2×C109 | C2×C16 |
| Fitting | C4×C8×C109 | C2 |
| socle | C22×C109 | C2×C8 |
| hypercenter | C4×C8 | D109 |
| hypocenter | C109 | C4⋊C16 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C2×C8 ◁ C4×C8 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^a=g^1081768 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊#13182004, #28360988, #28360990, … |
| maximal normal subgroup of | D4⋊#13182004, #28360988, #28360990, … |
| maximal quotient of | #28361096, #28361102, #28361110, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 368);