Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | Q16×C43⋊C8 |
| Sylow | C43 ⋊ C8×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D43 |
| commutator | C4×C43 | C22×C8 |
| Frattini | C42 | C22×D43 |
| Fitting | C4×Q16×C43 | C2 |
| socle | C22×C43 | C4×D4 |
| hypercenter | C4×Q16 | D43 |
| hypocenter | C43 | C8×Q16 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ C4×Q16 | |
164 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
644 conjugacy classes — view the full character table.
| maximal subgroup of | #25008321, SD32×C43⋊C8, #25008328, … |
| maximal normal subgroup of | #25008321, SD32×C43⋊C8, #25008328, … |
| maximal quotient of | #103×C43⋊C8, #107×C43⋊C8, #24990517, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 3317);