Finite Group DatabasebetaFinite Group Databasebeta| order | 5584 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C349 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #13063703 |
| commutator, hypocenter | C349 | C16 |
| Fitting | C4×C349 | C4 |
| socle | C2×C349 | C8 |
| LCS | G ▷ C349 | |
| UCS | C1 ◁ C4 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,349|a^2=b,b^2=c,c^2=d,e^a=e^213,e^b=e^348364 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#19150236, D349⋊C16, #26013713, … |
| maximal normal subgroup of | C2×#19150236, D349⋊C16, #26013713, … |
| maximal quotient of | #26013689, C2×#19150236 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5584, 43);