Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | #519×D43 |
| Fitting | C43×#519 ⋊ C2 |
| Sylow | C43 ⋊ C2×#519 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D43 |
| commutator | C2×C43 | C24×C4 |
| Fitting | C43×#519 | C2 |
| socle | C22×C43 | C25 |
| hypercenter | #519 | D43 |
| hypocenter | C43 | C2×#519 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #519 | |
1488 conjugacy classes of subgroups; only the 813 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 813 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
782 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1830, D43×#1857, #25097422, … |
| maximal normal subgroup of | D43×#1830, D43×#1857, #25097422, … |
| maximal quotient of | D43×#2274, D43×#2276, #25254844, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17698);