Finite Group DatabasebetaFinite Group Databasebeta| order | 5728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#15668258 |
| Fitting | C2×D4×C179 ⋊ C2 |
| Sylow | C179 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D179 |
| commutator | C2×C179 | C24 |
| Frattini | C2 | C23×D179 |
| Fitting | C2×D4×C179 | C2 |
| socle | C22×C179 | C23 |
| hypercenter | C2×D4 | D179 |
| hypocenter | C179 | C2×#41 |
| LCS | G ▷ C2×C179 ▷ C179 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
164 conjugacy classes of subgroups.
910 conjugacy classes — view the full character table.
| maximal subgroup of | #26038411, #26038420, #26038432, … |
| maximal normal subgroup of | #26038411, #26038420, #26038432, … |
| maximal quotient of | C2×#19153069, C2×#19153071, C2×(C22⋊D179)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5728, 188);