Finite Group DatabasebetaFinite Group Databasebeta| order | 5584 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#13063703 |
| Fitting | C4×C349 ⋊ C4 |
| Sylow | C349 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#13063703 |
| commutator, socle | C2×C349 | C2×C4 |
| Fitting | C4×C349 | C4 |
| hypercenter | C4 | #13063703 |
| hypocenter | C349 | C4⋊C4 |
| LCS | G ▷ C2×C349 ▷ C349 | |
| UCS | C1 ◁ C2 ◁ C4 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,349|a^2=d,b^2=c,b^a=bc,e^a=e^213,e^d=e^348358 conjugacy classes — view the full character table.
| maximal subgroup of | #26013701, #26013702, #26013707, … |
| maximal normal subgroup of | #26013701, #26013702, #26013707, … |
| maximal quotient of | (C2×#13063703)⋊C4, C4⋊#14584102, #26013706, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5584, 46);