Finite Group DatabasebetaFinite Group Databasebeta| order | 5728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#15668244 |
| Fitting | C2×D4×C179 ⋊ C2 |
| Sylow | C179 ⋊ C2×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊D179 |
| commutator | C4×C179 | C23 |
| Frattini | C4 | C22×D179 |
| Fitting | C2×D4×C179 | C2 |
| socle | C22×C179 | D4 |
| hypercenter | C2×D4 | D179 |
| hypocenter | C179 | C2×D8 |
| LCS | G ▷ C4×C179 ▷ C2×C179 ▷ C179 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×D4 | |
76 conjugacy classes of subgroups.
904 conjugacy classes — view the full character table.
| maximal subgroup of | #26038519, C4×#15668244, #26038548, … |
| maximal normal subgroup of | #26038519, C4×#15668244, #26038548, … |
| maximal quotient of | C2×#19153033, C2×#19153034, C2×#19153046, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5728, 156);