Finite Group DatabasebetaFinite Group Databasebeta| order | 9056 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C283 ⋊ #108 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22⋊D283 |
| commutator | C4×C283 | C2×C4 |
| Frattini | C2×C4 | C2×D283 |
| Fitting | M16×C283 | C2 |
| socle | C2×C283 | C4⋊C4 |
| hypercenter | M16 | D283 |
| hypocenter | C283 | #108 |
| LCS | G ▷ C4×C283 ▷ C2×C283 ▷ C283 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ M16 | |
30 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,283|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bc,c^a=ce,f^b=f^2821424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #108×D283, C2×#22583545, #31826512, … |
| maximal normal subgroup of | #108×D283, C2×#22583545, #31826512, … |
| maximal quotient of | #31826215, #31826217, #31826229, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9056, 81);