Finite Group DatabasebetaFinite Group Databasebeta| order | 5584 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#14584102 |
| derived, Sylow | C349 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #13063703 |
| commutator, hypocenter | C349 | C2×C8 |
| Frattini | C2 | C2×#13063703 |
| Fitting, socle | C22×C349 | C4 |
| LCS | G ▷ C349 | |
| UCS | C1 ◁ C22 | |
22 conjugacy classes of subgroups.
364 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#14584102, #26013694, C22⋊#14584102, … |
| maximal normal subgroup of | C4×#14584102, #26013694, C22⋊#14584102, … |
| maximal quotient of | C4×#14584102, C22⋊#14584102, C4⋊#14584102, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5584, 47);