Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #1623 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13063293 |
| commutator | C42×C43 | C23 |
| Frattini | C42 | C22×D43 |
| Fitting | C43×#492 | C2 |
| socle | C22×C43 | #120 |
| hypercenter | #492 | D43 |
| hypocenter | C43 | #1623 |
| LCS | G ▷ C42×C43 ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #492 | |
228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|b^2=f,c^2=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,d^b=df,e^b=eg,d^c=dg,e^c=eg,h^c=h^42488 conjugacy classes — view the full character table.
| maximal subgroup of | #24984427, #24984429, #25017366, … |
| maximal normal subgroup of | #24984427, #24984429, #25017366, … |
| maximal quotient of | #24985335, #24985372, #24985379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 3586);