Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#14583247 |
| Fitting | C2×C4⋊Q8×C43 ⋊ C2 |
| Sylow | C43 ⋊ C2×#486 |
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 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.
632 conjugacy classes — view the full character table.
| maximal subgroup of | #24991843, #24991849, #24991877, … |
| maximal normal subgroup of | #24991843, #24991849, #24991877, … |
| maximal quotient of | C2×#19134722, C2×#19135277, C2×#19135400, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 14817);