Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C43 ⋊ C2 |
| Sylow | C43 ⋊ #2334 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator | C22×C43 | C23×C4 |
| Fitting | C4×C4⋊C4×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C4×C4⋊C4 | D43 |
| hypocenter | C43 | #2334 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 | |
476 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=g,b^2=g,c^2=e,d^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,h^c=h^42884 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#2334, C2×#19137364, #25255519, … |
| maximal normal subgroup of | D43×#2334, C2×#19137364, #25255519, … |
| maximal quotient of | #25017869, #25017923, #25017926, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 7279);