Finite Group DatabasebetaFinite Group Databasebeta| order | 5536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#14583835 |
| Sylow | C173 ⋊ C2×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#10621924 |
| commutator | C2×C173 | C22×C4 |
| Frattini | C2 | C22×#10621924 |
| Fitting | C23×C173 | C4 |
| socle | C22×C173 | C2×C4 |
| hypercenter | C23 | #10621924 |
| hypocenter | C173 | C2×M16 |
| LCS | G ▷ C2×C173 ▷ C173 | |
| UCS | C1 ◁ C22 ◁ C23 | |
68 conjugacy classes of subgroups.
364 conjugacy classes — view the full character table.
| maximal subgroup of | #26012371, #26012372, C4×#14583835, … |
| maximal normal subgroup of | #26012371, #26012372, C4×#14583835, … |
| maximal quotient of | C2×#19149734, C4×#14583835, C2×C22⋊#13063443, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5536, 230);