Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C22×C4 |
| unambiguous semidirect product | C43⋊#1273 |
| Sylow | C43 ⋊ #1273 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C42 | C2×D43 |
| commutator | C2×C43 | C82 |
| Fitting | C2×C4×C8×C43 | C2 |
| socle | C23×C43 | C42 |
| hypercenter | C2×C4×C8 | D43 |
| hypocenter | C43 | #1273 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C42 ◁ C2×C4×C8 | |
212 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bc,h^b=h^421424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24983369, #24983370, #24983382, … |
| maximal normal subgroup of | #24983369, #24983370, #24983382, … |
| maximal quotient of | C43⋊#7014, #24983124, #24983125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2337);