Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C43×#451 ⋊ C2 |
| Sylow | C43 ⋊ D4×Q16 |
472 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=g,b^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,e^d=eg,h^d=h^42434 conjugacy classes — view the full character table.
| maximal subgroup of | D4×Q16×D43, C2×#19146340, #25971885, … |
| maximal normal subgroup of | D4×Q16×D43, C2×#19146340, #25971885, … |
| maximal quotient of | #25086777, #25086782, #25086787, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 16255);