Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
| unambiguous semidirect product | Dic43⋊#95 |
| Sylow | C43 ⋊ C4⋊#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D43 |
| commutator | C22×C43 | C2×C42 |
| Fitting | C2×#95×C43 | C2 |
| socle | C24×C43 | C23 |
| hypercenter | C2×#95 | D43 |
| hypocenter | C43 | C4⋊#95 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
656 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=f,b^2=g,c^2=e,b^a=bd,c^a=ce,h^c=h^42896 conjugacy classes — view the full character table.
| maximal subgroup of | #24989318, #24989319, #24989323, … |
| maximal normal subgroup of | #24989318, #24989319, #24989323, … |
| maximal quotient of | #24984516, #24984523, #25002382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2738);