Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C109 ⋊ #379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D109 |
| commutator | C22×C109 | C22×C4 |
| Fitting | C25×C109 | C2 |
| socle | C23×C109 | C23 |
| hypercenter | C25 | D109 |
| hypocenter | C109 | #379 |
| LCS | G ▷ C22×C109 ▷ C109 | |
| UCS | C1 ◁ C23 ◁ C25 | |
506 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=f,b^a=bd,c^a=ce,g^a=g^1081756 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28360936, #28362946, #28362947, … |
| maximal normal subgroup of | #28360936, #28362946, #28362947, … |
| maximal quotient of | #28361255, #28361273, #28361303, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 405);