Finite Group DatabasebetaFinite Group Databasebeta| order | 5584 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D4×C349 ⋊ C2 |
| Sylow | C349 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D349 |
| commutator | C4×C349 | C22 |
| Frattini | C4 | C2×D349 |
| Fitting | D4×C349 | C2 |
| socle | C2×C349 | D4 |
| hypercenter | D4 | D349 |
| hypocenter | C349 | D8 |
| LCS | G ▷ C4×C349 ▷ C2×C349 ▷ C349 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
22 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,349|c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^348877 conjugacy classes — view the full character table.
| maximal subgroup of | D8×D349, C2×#19150218, #26013659, … |
| maximal normal subgroup of | D8×D349, C2×#19150218, #26013659, … |
| maximal quotient of | #26013559, #26013560, #26013572, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5584, 25);