Finite Group DatabasebetaFinite Group Databasebeta| order | 5584 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×Dic698 |
| unambiguous semidirect product | (C2×C349)⋊Q8 |
| Sylow | C349 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D349 |
| commutator | C2×C349 | C23 |
| Frattini | C2 | C22×D349 |
| Fitting | C2×C4×C349 | C2 |
| socle | C22×C349 | C22 |
| hypercenter | C2×C4 | D349 |
| hypocenter | C349 | C2×Q8 |
| LCS | G ▷ C2×C349 ▷ C349 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
38 conjugacy classes of subgroups.
1402 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26013557, #26013562, #26013564, … |
| maximal normal subgroup of | #26013557, #26013562, #26013564, … |
| maximal quotient of | C2×#19150212, C2×C4⋊Dic349, C4×Dic698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5584, 38);