Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D109⋊(C4⋊C8) |
| Sylow | C109 ⋊ C2×C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×#89137 |
| commutator | C2×C109 | C22×C8 |
| Frattini | C22 | C22×#89137 |
| Fitting | C42×C109 | C4 |
| socle | C22×C109 | C22×C4 |
| hypercenter | C42 | #89137 |
| hypocenter | C109 | C2×C4⋊C8 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
138 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=e,b^2=d,e^2=f,b^a=bd,g^a=g^33,g^c=g^108,g^e=g^108472 conjugacy classes — view the full character table.
| maximal subgroup of | #28377861, #28377867, #28377896, … |
| maximal normal subgroup of | #28377861, #28377867, #28377896, … |
| maximal quotient of | D109⋊#334, D109⋊#335, #28378580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1550);