Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C109 ⋊ M64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×#89137 |
| commutator, socle | C2×C109 | C2×C16 |
| Fitting | C16×C109 | C4 |
| hypercenter | C16 | #89137 |
| hypocenter | C109 | M64 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C8 ◁ C16 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=c,c^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^33,g^b=g^108,g^c=g^108472 conjugacy classes — view the full character table.
| maximal subgroup of | #28378141, #28378142, #28378185, … |
| maximal normal subgroup of | #28378141, #28378142, #28378185, … |
| maximal quotient of | #28378140, #28378146, #28378190, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1482);