Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | D4×C43⋊C16 |
| Sylow | C43 ⋊ D4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D43 |
| commutator | C2×C43 | C22×C16 |
| Fitting | C8×D4×C43 | C2 |
| socle | C22×C43 | C22×C8 |
| hypercenter | C8×D4 | D43 |
| hypocenter | C43 | D4×C16 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C8 ◁ C8×D4 | |
174 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
920 conjugacy classes — view the full character table.
| maximal subgroup of | #25008299, D8×C43⋊C16, #25008304, … |
| maximal normal subgroup of | #25008299, D8×C43⋊C16, #25008304, … |
| maximal quotient of | D8×C43⋊C16, SD16×C43⋊C16, Q16×C43⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6330);