Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#13063239 |
| Fitting | C22×C22⋊C4×C43 ⋊ C2 |
| Sylow | C43 ⋊ C22×#99 |
1112 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 269 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 | #25001938, #25001941, #25001983, … |
| maximal normal subgroup of | #25001938, #25001941, #25001983, … |
| maximal quotient of | C22×#14582622, C22×#14582624, C2×#19132911, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 12962);