Finite Group DatabasebetaFinite Group Databasebeta| order | 5584 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊Dic349 |
| Sylow | C349 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D349 |
| commutator | C2×C349 | C2×C4 |
| Fitting | C23×C349 | C2 |
| socle | C22×C349 | C22 |
| hypercenter | C23 | D349 |
| hypocenter | C349 | C22⋊C4 |
| LCS | G ▷ C2×C349 ▷ C349 | |
| UCS | C1 ◁ C22 ◁ C23 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,349|a^2=d,b^a=bc,e^a=e^3481402 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26013553, #26013554, C22⋊C4×D349, … |
| maximal normal subgroup of | #26013553, #26013554, C22⋊C4×D349, … |
| maximal quotient of | #26013546, C22⋊#14584095, #26013554, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5584, 18);