Finite Group DatabasebetaFinite Group Databasebeta| order | 5536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#10621924 |
| unambiguous semidirect product | D173⋊C42 |
| Fitting | C2×C4×C173 ⋊ C4 |
| derived, Sylow | C173 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #10621924 |
| commutator, hypocenter | C173 | C2×C42 |
| Frattini | C2 | C22×#10621924 |
| Fitting | C2×C4×C173 | C4 |
| socle | C22×C173 | C2×C4 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C2×C4 | |
108 conjugacy classes of subgroups.
376 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#10621924)⋊C8, #26012361, #26012363, … |
| maximal normal subgroup of | (C2×#10621924)⋊C8, #26012361, #26012363, … |
| maximal quotient of | C42×#10621924, C2×(C2×#10621924)⋊C4, #26012427, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5536, 222);