Finite Group DatabasebetaFinite Group Databasebeta| order | 5536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#14583816 |
| Sylow | C173 ⋊ C2×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊D173 |
| commutator | C4×C173 | C23 |
| Frattini | C4 | C22×D173 |
| Fitting | C2×Q8×C173 | C2 |
| socle | C22×C173 | D4 |
| hypercenter | C2×Q8 | D173 |
| hypocenter | C173 | C2×Q16 |
| LCS | G ▷ C4×C173 ▷ C2×C173 ▷ C173 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×Q8 | |
60 conjugacy classes of subgroups.
874 conjugacy classes — view the full character table.
| maximal subgroup of | #26011583, C4×#14583816, #26011595, … |
| maximal normal subgroup of | #26011583, C4×#14583816, #26011595, … |
| maximal quotient of | C2×#19149602, C2×#19149603, C2×#19149612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5536, 163);