Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #3312 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D172 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#435 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #435 | D43 |
| hypocenter | C43 | #3312 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ #435 | |
376 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=e,b^2=g,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^42,c^b=cg,d^b=de,f^c=fg,h^c=h^42617 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3312, C2×#19146648, #25973374, … |
| maximal normal subgroup of | D43×#3312, C2×#19146648, #25973374, … |
| maximal quotient of | #25112169, #25112887, #25113664, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 16563);