Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #1890 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13063295 |
| commutator | C23×C43 | C22×C4 |
| Frattini | C24 | C22×D43 |
| Fitting | C2×#99×C43 | C2 |
| socle | C22×C43 | #120 |
| hypercenter | C2×#99 | D43 |
| hypocenter | C43 | #1890 |
| LCS | G ▷ C23×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C2×#99 | |
386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 89 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,b^2=dfg,b^a=bd,c^a=ce,e^a=eg,e^b=eg,h^b=h^42,d^c=dg,f^c=fg494 conjugacy classes — view the full character table.
| maximal subgroup of | #25012360, #25012362, #25012400, … |
| maximal normal subgroup of | #25012360, #25012362, #25012400, … |
| maximal quotient of | #24991285, #24991295, #24991574, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4921);