Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C22⋊C4×C43⋊C8 |
| Sylow | C43 ⋊ C8×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D43 |
| commutator | C2×C43 | C2×C4×C8 |
| Fitting | C4×C22⋊C4×C43 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | C4×C22⋊C4 | D43 |
| hypocenter | C43 | C8×C22⋊C4 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C22⋊C4 | |
384 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 181 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 | #24987137, #99×C43⋊C8, #24987147, … |
| maximal normal subgroup of | #24987137, #99×C43⋊C8, #24987147, … |
| maximal quotient of | C22⋊C8×C43⋊C8, #24987072, #24987088, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4283);