Finite Group DatabasebetaFinite Group Databasebeta| order | 1056 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C11 ⋊ D16 |
| Sylow | C11 ⋊ #826 |
| Sylow | C3 ⋊ D176 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #10587142 |
| commutator, Fitting, cosocle | C3×C8×C11 | C22 |
| Frattini, hypercenter | C8 | D3×D11 |
| socle | C2×C3×C11 | D8 |
| hypocenter | C3×C11 | D16 |
| LCS | G ▷ C3×C8×C11 ▷ C3×C4×C11 ▷ C2×C3×C11 ▷ C3×C11 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 528 |
Polycyclic presentation:
2^5,3,11|b^2=cd,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,g^a=g^10,f^b=f^2138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1056, 12);