Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #2744 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C43×#381 | C2 |
| hypercenter | #381 | D43 |
| hypocenter | C43 | #2744 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #381 | |
392 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=efg,b^2=f,c^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^42,c^b=cg,d^b=de620 conjugacy classes — view the full character table.
| maximal subgroup of | #25303718, #25303731, #25303817, … |
| maximal normal subgroup of | #25303718, #25303731, #25303817, … |
| maximal quotient of | #25024011, #25024067, #25024225, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 11664);