Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C43×#577 ⋊ C2 |
| Sylow | C43 ⋊ #3291 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×C22⋊D43 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#577 | C2 |
| socle | C2×C43 | D42 |
| hypercenter | #577 | D43 |
| hypocenter | C43 | #3291 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #577 | |
460 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,c^b=cg,d^b=de,e^b=eg,f^c=fg,h^c=h^42,e^d=eg491 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3291, C2×#19146386, #25972830, … |
| maximal normal subgroup of | D43×#3291, C2×#19146386, #25972830, … |
| maximal quotient of | #25087869, #25087871, #25087915, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 16301);