Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | Q8×C43⋊C16 |
| Sylow | C43 ⋊ Q8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D43 |
| commutator | C2×C43 | C22×C16 |
| Fitting | C8×Q8×C43 | C2 |
| socle | C22×C43 | C22×C8 |
| hypercenter | C8×Q8 | D43 |
| hypocenter | C43 | Q8×C16 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C8 ◁ C8×Q8 | |
134 conjugacy classes of subgroups.
920 conjugacy classes — view the full character table.
| maximal subgroup of | #25008360, SD16×C43⋊C16, #25008374, … |
| maximal normal subgroup of | #25008360, SD16×C43⋊C16, #25008374, … |
| maximal quotient of | C4⋊C4×C43⋊C16, #25014214, #25014598, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6414);