Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C109 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #89137 |
| commutator, hypocenter | C109 | C4×C16 |
| Frattini | C2×C4 | C2×#89137 |
| Fitting | C2×C8×C109 | C4 |
| socle | C22×C109 | C2×C8 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C2×C8 | |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=c,b^2=d,c^2=e,e^2=f,g^a=g^33,g^b=g^108,g^c=g^108496 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#11724786, #28377943, #11724786⋊C16, … |
| maximal normal subgroup of | C16×#11724786, #28377943, #11724786⋊C16, … |
| maximal quotient of | C8×#13182032, #28377947, #28378071, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1435);