Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×#117×C43 ⋊ C2 |
| Sylow | C43 ⋊ #3428 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D43 |
| commutator | C2×C43 | C24×C4 |
| Frattini | C22 | C24×D43 |
| Fitting | C2×#117×C43 | C2 |
| socle | C22×C43 | C25 |
| hypercenter | C2×#117 | D43 |
| hypocenter | C43 | #3428 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#117 | |
1540 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=g,e^2=f,b^a=bf,d^a=df,c^b=cf,h^c=h^42908 conjugacy classes — view the full character table.
| maximal subgroup of | #25001928, #25001931, #25001948, … |
| maximal normal subgroup of | #25001928, #25001931, #25001948, … |
| maximal quotient of | #25254809, #25254811, #25254823, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17711);