Finite Group DatabasebetaFinite Group Databasebeta| order | 5584 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C349 ⋊ C2 |
| Sylow | C349 ⋊ SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D1396 |
| commutator | C4×C349 | C22 |
| Frattini | C4 | C2×D349 |
| Fitting | C8×C349 | C2 |
| socle | C2×C349 | D4 |
| hypercenter | C8 | D349 |
| hypocenter | C349 | SD16 |
| LCS | G ▷ C4×C349 ▷ C2×C349 ▷ C349 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,349|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^348,c^b=cd,e^b=e^3481399 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16×D349, C2×#19150222, #26013660, … |
| maximal normal subgroup of | SD16×D349, C2×#19150222, #26013660, … |
| maximal quotient of | #26013561, #26013564, #26013571, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5584, 29);