Finite Group DatabasebetaFinite Group Databasebeta| order | 5584 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C349 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#13063703 |
| commutator, socle | C2×C349 | C2×C4 |
| Fitting | C4×C349 | C4 |
| hypercenter | C4 | #13063703 |
| hypocenter | C349 | M16 |
| LCS | G ▷ C2×C349 ▷ C349 | |
| UCS | C1 ◁ C2 ◁ C4 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,349|a^2=c,c^2=d,b^a=bd,e^a=e^213,e^b=e^348,e^c=e^348358 conjugacy classes — view the full character table.
| maximal subgroup of | #26013703, #26013704, #26013709, … |
| maximal normal subgroup of | #26013703, #26013704, #26013709, … |
| maximal quotient of | #26013694, #26013696, C4⋊#14584102, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5584, 50);