Finite Group DatabasebetaFinite Group Databasebeta| order | 5584 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×D349 |
| Fitting | C8×C349 ⋊ C2 |
| derived, Sylow | C349 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D349 |
| commutator, hypocenter | C349 | C2×C8 |
| Frattini | C4 | C2×D349 |
| Fitting | C8×C349 | C2 |
| socle | C2×C349 | C2×C4 |
| LCS | G ▷ C349 | |
| UCS | C1 ◁ C8 | |
22 conjugacy classes of subgroups.
1408 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×D349, #26013578, C2×C8×D349, … |
| maximal normal subgroup of | C16×D349, #26013578, C2×C8×D349, … |
| maximal quotient of | C8×Dic349, #26013551, #26013568, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5584, 21);