Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C8×C109 ⋊ C4 |
| Sylow | C109 ⋊ #405 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C2×#89137 |
| commutator, socle | C2×C109 | C2×C42 |
| Frattini | C4 | C22×#89137 |
| Fitting | C2×C8×C109 | C4 |
| hypercenter | C2×C8 | #89137 |
| hypocenter | C109 | #405 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C8 ◁ C2×C8 | |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,b^2=e,d^2=f,c^b=cf,g^b=g^33,g^e=g^108472 conjugacy classes — view the full character table.
| maximal subgroup of | #28378081, #28378084, #28378085, … |
| maximal normal subgroup of | #28378081, #28378084, #28378085, … |
| maximal quotient of | C8×#13182038, C8×#13182039, #28378235, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1512);