Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#14583009 |
| Fitting | C2×C4×D4×C43 ⋊ C2 |
| Sylow | C43 ⋊ C2×#442 |
608 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 205 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 | #24992019, #24992020, #24992022, … |
| maximal normal subgroup of | #24992019, #24992020, #24992022, … |
| maximal quotient of | C2×#19133417, C2×#19133457, C2×#19133459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13301);