Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×C4×D344 |
| Fitting | C2×C4×C8×C43 ⋊ C2 |
| Sylow | C43 ⋊ C2×C4×D8 |
616 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24991171, #24991173, #24991199, … |
| maximal normal subgroup of | #24991171, #24991173, #24991199, … |
| maximal quotient of | C2×C8×D344, C2×#19133426, C2×#19133481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13262);