Finite Group DatabasebetaFinite Group Databasebeta| order | 5536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×D692 |
| Fitting | C42×C173 ⋊ C2 |
| Sylow | C173 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D173 |
| commutator | C2×C173 | C22×C4 |
| Frattini | C22 | C22×D173 |
| Fitting | C42×C173 | C2 |
| socle | C22×C173 | C23 |
| hypercenter | C42 | D173 |
| hypocenter | C173 | C4×D4 |
| LCS | G ▷ C2×C173 ▷ C173 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
94 conjugacy classes of subgroups.
1396 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26011218, #26011220, #26011556, … |
| maximal normal subgroup of | #26011218, #26011220, #26011556, … |
| maximal quotient of | C4×#14583803, C4×C4⋊Dic173, #26011365, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5536, 110);