Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×M16×C43 ⋊ C2 |
| Sylow | C43 ⋊ #2873 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D43 |
| commutator | C2×C43 | C22×C42 |
| Fitting | C4×M16×C43 | C2 |
| socle | C22×C43 | C23×C4 |
| hypercenter | C4×M16 | D43 |
| hypocenter | C43 | #2873 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C4×M16 | |
564 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=e,b^2=f,e^2=g,d^a=dg,c^b=cg,h^c=h^42908 conjugacy classes — view the full character table.
| maximal subgroup of | #24993929, #24993931, #24993934, … |
| maximal normal subgroup of | #24993929, #24993931, #24993934, … |
| maximal quotient of | #25062179, #25062203, #25062229, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 12927);