Finite Group DatabasebetaFinite Group Databasebeta| order | 5536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C173 ⋊ C2 |
| Sylow | C173 ⋊ C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D173 |
| commutator, socle | C22×C173 | C23 |
| Fitting | C4⋊C4×C173 | C2 |
| hypercenter | C4⋊C4 | D173 |
| hypocenter | C173 | C22⋊Q8 |
| LCS | G ▷ C22×C173 ▷ C173 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,173|a^2=d,b^2=d,b^a=bd,c^a=ce,f^b=f^172,f^c=f^172874 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊Q8×D173, C2×#19149657, #26011999, … |
| maximal normal subgroup of | C22⋊Q8×D173, C2×#19149657, #26011999, … |
| maximal quotient of | #26011350, #26011362, #26011365, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5536, 124);