Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×#13063239 |
| Fitting | C4×C22⋊C4×C43 ⋊ C2 |
| Sylow | C43 ⋊ C4×#99 |
412 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
884 conjugacy classes — view the full character table.
| maximal subgroup of | #24987137, C8×#13063239, #24987142, … |
| maximal normal subgroup of | #24987137, C8×#13063239, #24987142, … |
| maximal quotient of | C4×#14582622, C4×#14582624, #24987108, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4299);