Finite Group DatabasebetaFinite Group Databasebeta| order | 5536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C42×C173 ⋊ C2 |
| Sylow | C173 ⋊ #104 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | D692 |
| commutator | C4×C173 | C2×C4 |
| Frattini | C2×C4 | C2×D173 |
| Fitting | C42×C173 | C2 |
| socle | C2×C173 | C22⋊C4 |
| hypercenter | C42 | D173 |
| hypocenter | C173 | #104 |
| LCS | G ▷ C4×C173 ▷ C2×C173 ▷ C173 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ C42 | |
44 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,173|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^172,c^b=ce,f^b=f^1721390 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #104×D173, C2×#19149607, #26011506, … |
| maximal normal subgroup of | #104×D173, C2×#19149607, #26011506, … |
| maximal quotient of | #26011220, #26011223, #26011224, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5536, 74);