Finite Group DatabasebetaFinite Group Databasebeta| order | 5584 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4×C349 ⋊ C2 |
| Sylow | C349 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D349 |
| commutator, socle | C2×C349 | C23 |
| Fitting | D4×C349 | C2 |
| hypercenter | D4 | D349 |
| hypocenter | C349 | #41 |
| LCS | G ▷ C2×C349 ▷ C349 | |
| UCS | C1 ◁ C2 ◁ D4 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,349|c^2=d,b^a=bd,e^c=e^348880 conjugacy classes — view the full character table.
| maximal subgroup of | #26013658, #26013660, #26013663, … |
| maximal normal subgroup of | #26013658, #26013660, #26013663, … |
| maximal quotient of | #26013595, #26013597, #26013599, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5584, 39);