Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C43 ⋊ #1827 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13063281 |
| commutator | C2×C4×C43 | C22×C4 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#413 | C2 |
| socle | C2×C43 | #381 |
| hypercenter | #413 | D43 |
| hypocenter | C43 | #1827 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #413 | |
262 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|a^2=f,c^2=d,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^42,f^b=fg,f^c=fg,h^c=h^42494 conjugacy classes — view the full character table.
| maximal subgroup of | #25012181, #25012185, #25012186, … |
| maximal normal subgroup of | #25012181, #25012185, #25012186, … |
| maximal quotient of | #24990038, #24990042, #24990046, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4615);