Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | Q8×C11×#41 ⋊ C2 |
| Sylow | C11 ⋊ #62805 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C24×D11 |
| commutator, socle, cosocle | C22×C11 | C26 |
| Frattini | C22 | C25×D11 |
| Fitting | Q8×C11×#41 | C2 |
| hypercenter | Q8×#41 | D11 |
| hypocenter | C11 | #62805 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C2×C4 ◁ Q8×#41 | |
7104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^8,11|a^2=h,e^2=h,f^2=g,b^a=bg,c^a=ch,e^a=eh,d^c=dh,i^c=i^10,i^d=i^10,i^e=i^10338 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1078019);