Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C43 ⋊ #1726 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D43 |
| commutator | C2×C43 | C43 |
| Fitting | C43×#376 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | #376 | D43 |
| hypocenter | C43 | #1726 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ #376 | |
328 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=d,b^2=e,c^2=f,d^2=g,h^a=h^42,c^b=cg920 conjugacy classes — view the full character table.
| maximal subgroup of | #24987035, #24987039, #24987043, … |
| maximal normal subgroup of | #24987035, #24987039, #24987043, … |
| maximal quotient of | #24985951, #24985954, #24985960, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4197);