Finite Group DatabasebetaFinite Group Databasebeta| order | 9056 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C283 ⋊ C2 |
| Sylow | C283 ⋊ #123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D283 |
| commutator, socle | C22×C283 | C23 |
| Fitting | C4⋊C4×C283 | C2 |
| hypercenter | C4⋊C4 | D283 |
| hypocenter | C283 | #123 |
| LCS | G ▷ C22×C283 ▷ C283 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,283|c^2=d,b^a=bd,c^a=ce,f^a=f^282,f^b=f^2821424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #123×D283, C2×#22583595, #31826974, … |
| maximal normal subgroup of | #123×D283, C2×#22583595, #31826974, … |
| maximal quotient of | #31826327, #31826336, #31826343, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9056, 131);