Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #2331 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator | C22×C43 | C23×C4 |
| Fitting | C43×#391 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | #391 | D43 |
| hypocenter | C43 | #2331 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #391 | |
460 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=g,b^2=fg,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,h^d=h^42632 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#2331, C2×#19137338, #25255438, … |
| maximal normal subgroup of | D43×#2331, C2×#19137338, #25255438, … |
| maximal quotient of | #25017855, #25017883, #25017887, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 7253);