Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #1375 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic43 |
| commutator | C4×C43 | C4×C8 |
| Frattini | C22×C8 | C2×D43 |
| Fitting | C2×#97×C43 | C2 |
| socle | C22×C43 | #97 |
| hypercenter | C2×#97 | D43 |
| hypocenter | C43 | #1375 |
| LCS | G ▷ C4×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#97 | |
140 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,e^a=eg,h^a=h^42,d^b=dg884 conjugacy classes — view the full character table.
| maximal subgroup of | #24983354, #24983355, #24983374, … |
| maximal normal subgroup of | #24983354, #24983355, #24983374, … |
| maximal quotient of | #24983427, #24983439, #24983446, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2590);