Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C109 ⋊ #376 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D109 |
| commutator | C2×C109 | C2×C42 |
| Frattini | C23 | C22×D109 |
| Fitting | C2×C42×C109 | C2 |
| socle | C23×C109 | C23 |
| hypercenter | C2×C42 | D109 |
| hypocenter | C109 | #376 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
178 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=e,b^2=f,c^2=d,b^a=bd,g^b=g^1081768 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28360860, #28360924, #28360926, … |
| maximal normal subgroup of | #28360860, #28360924, #28360926, … |
| maximal quotient of | C4×#16812606, #28361257, #28361259, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 395);