Finite Group DatabasebetaFinite Group Databasebeta| order | 9056 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#17985380 |
| Sylow | C283 ⋊ C2×SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊D283 |
| commutator | C4×C283 | C23 |
| Frattini | C4 | C22×D283 |
| Fitting | C2×D4×C283 | C2 |
| socle | C22×C283 | D4 |
| hypercenter | C2×D4 | D283 |
| hypocenter | C283 | C2×SD16 |
| LCS | G ▷ C4×C283 ▷ C2×C283 ▷ C283 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×D4 | |
68 conjugacy classes of subgroups.
1424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#17985380, #31826556, #31826562, … |
| maximal normal subgroup of | C4×#17985380, #31826556, #31826562, … |
| maximal quotient of | C2×#22583531, C2×#22583533, C2×#22583541, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9056, 160);