Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | C2×C11×#532 ⋊ C2 |
| Sylow | C11 ⋊ #62748 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C24×D11 |
| commutator, socle, cosocle | C22×C11 | C26 |
| Frattini | C22 | C25×D11 |
| Fitting | C2×C11×#532 | C2 |
| hypercenter | C2×#532 | D11 |
| hypocenter | C11 | #62748 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#532 | |
7280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^8,11|d^2=h,f^2=g,b^a=bg,c^a=ch,d^a=dg,e^a=eh,i^a=i^10,c^b=cg,d^b=dh356 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1077237);