Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C22⋊C8×Dic43 |
| Sylow | C43 ⋊ C4×C22⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D43 |
| commutator | C2×C43 | C2×C4×C8 |
| Fitting | C2×C22⋊C8×C43 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | C2×C22⋊C8 | D43 |
| hypocenter | C43 | C4×C22⋊C8 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C22⋊C8 | |
436 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 177 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 | #24987098, #323×Dic43, #24987102, … |
| maximal normal subgroup of | #24987098, #323×Dic43, #24987102, … |
| maximal quotient of | C22⋊C8×C43⋊C8, #24987068, #24987077, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4270);