Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C109 ⋊ #322 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C2×D109 |
| commutator | C2×C109 | C4×C8 |
| Fitting | C4×C8×C109 | C2 |
| socle | C22×C109 | C42 |
| hypercenter | C4×C8 | D109 |
| hypocenter | C109 | #322 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C42 ◁ C4×C8 | |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=c,b^2=d,c^2=e,d^2=f,b^a=be,g^b=g^1081768 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28360952, #28360954, #28361007, … |
| maximal normal subgroup of | #28360952, #28360954, #28361007, … |
| maximal quotient of | #28360859, #28360950, #28360952, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 270);