Finite Group DatabasebetaFinite Group Databasebeta| order | 5792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#15668452 |
| derived, Sylow | C181 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #10624382 |
| commutator, hypocenter | C181 | C2×C16 |
| Frattini | C4 | C2×#10624382 |
| Fitting | C2×C4×C181 | C4 |
| socle | C22×C181 | C8 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C2×C4 | |
28 conjugacy classes of subgroups.
392 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#15668452, #26042165, #26042167, … |
| maximal normal subgroup of | C4×#15668452, #26042165, #26042167, … |
| maximal quotient of | C4×#15668452, C22⋊#15668452, C4⋊#15668452, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5792, 218);